# Questions tagged [completing-the-square]

Questions on the algebraic operation of completing the square. Should probably be used with the (algebra-precalculus) tag.

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### A Complete Guide to Completing The Square

I've noticed recently that many people on this site are not so familiar with the method of completing the square with quadratic equations. So, this question and my answer is a full explanation on ...
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### Frobenius norm: completing squares and minimizing

I would like to minimize the following quantity: $Q = \left\lVert{X - C}\right\rVert^2_F + a\left\lVert{X - I}\right\rVert^2_F$ Where $X\in\mathbb R^{n\times n}$ is unknown, $C\in\mathbb R^{n\times n}$...
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### Completing the square of complicated expression (answer available)

I would like to rewrite the following expression \begin{align} \frac{1}{\sigma_{\theta}^{2}}\sum_{i=1}^{I}(\theta_{i}-\mu)^{2} + \frac{1}{\sigma_{0}^{2}}(\mu-\mu_{0})^{2} \end{align} as a square ...
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### How to convert 3 variable quadratic form into a sum of squares?

How do I convert the 3-variable quadratic form q(x₁ x₂ x₃) = row vector [x₁ x₂ x₃] multiplied by [a₁₁ a₁₂ a₁₃ a₂₁ a₂₂ a₂₃ a₃₁ a₃₂ a₃₃]₃ₓ₃ matrix multiplied by column vector [x₁ x₂ x₃] into the ...
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### hey !! i did part a but i am stuck with part b..Can anyone help me out? [closed]

(a) Write the quadratic expression $ax^2+bx+c$ in the form $a(x+h)^2+k$ for suitable values of $h$ and $k$ in terms of $a$, $b$, and $c$. (b) When does the equation $a(x+h)^2+k=0$ have solutions? ...
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### How can one show that $\sqrt{5+2\sqrt{6}}=\sqrt{3}+\sqrt{2}$ is true? [closed]

I was searching for some knowledge about algebra and found something interesting I found a an equation of 4th order that looks like this $x^4-10x^2+1 = 0$ in the article that I was reading, I found ...
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### Completing the square of: $y^2-xz$

How can I complete the square of the following monomial: $y^2-xz$ to obtain the sum of 3 squares of the form: $y'^2-z'^2-x'^2$. Any suggestions for finding $x',y'$ and $z'$??
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### Completing the Square with a quartic polynomial

Find all integers $n$ for which $81\frac{n^4}{4}-2017n^2+81$ is a prime. I know completing the square helps with this problem, but I'm not how completing the square is going to get me to the right ...
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### Solving this quadratic equation by completing the square?

$-\frac{2}{3}x^{2} - x +2 = 0$ Here's what I did: However, the textbook answer is $x = -2.6, x = 1.1$. What did I do wrong?
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### How to solve $9x^2+6x-5$ by “completing the square” method so that we can get the result as $(3x+1)^2 +6$? [closed]

I am having trouble getting the answer using "completing the square" method. Please explain all the steps.
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### Quadratic Function: possible value of c

I have $f(x)=x^2-2bx+c$ If the minimum value of the function is 6, what is the possible value of c. I tried$$f(x)=(x-b)^2-b^2+c$$ $$b^2=c-6$$ I couldn't solve for the value of c.
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### Completing the square of $(m^2 + n^2)$

I'm attempting to complete the square of $m^2 + n^2$, How would I do this? I am not understanding, as most resources refer to a polynomial with $x$ as it's variable and every term is in terms of $x$. ...
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### How to get $\frac{2}{3}(3x-5)^{2}+\frac{19}{3}$ from this expression $6x^{2}-20x+23$.

I'm trying to figure out how to get $\frac{2}{3}(3x-5)^{2}+\frac{19}{3}$ from this expression $6x^{2}-20x+23$. Hints?
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I need to integrate the following using trigonometric substitution. I also know that I need to do the following by completing the square in the denominator, but I can't seem to figure it out. $$\int \... 2answers 667 views ### Find inverse of a quadratic polynomial by 'completing the square' I have been asked to find the inverse of an equation that has the form y=ax^2 + by -c EDIT: Which is y=4x^2+ 8x -3 in the graph below Using a graphing calculator, and trial and error, I can find ... 2answers 105 views ### Solve y = \frac{x^6}{6} + \frac{1}{16x^4} by completing a perfect square, with a given domain. [closed] Problem:$$y = \frac{x^6}{6} + \frac{1}{16x^4} \text{ for } 4 \le x \le 25 Solve by completing the square and use regular anti-derivatives. Not even sure where to begin. I'm taking online classes ...
How crucial is this skill or form of writing and polynomial function? Can't we just always use the $-b/2a$ trick for the $x$ intercept and just plug it back into the function to find the $y$?