Questions tagged [completing-the-square]

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

94 questions
Filter by
Sorted by
Tagged with
205 views

50 views

How to find the minimum of $xy$ from the equation $2x+y+6=xy$ , $x,y>0$

I have tried doing factoring and completing the square and also AM-GM $(2-y)(x-1)=-8$ $xy=2x+y+6≥\sqrt{12xy}$
85 views

93 views

How to factorize $2x^2 + 2x + 1$?

How to factorize $2x^2 + 2x + 1 = 0$ into $2(x + 0.5)^2 + 0.5$ ? What is the process behind this factorization? Edit: Thanks guys, have updated this post. Updated the tag to complete the square.
109 views

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, $C\in\mathbb R^{n\times n}$...
26 views

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 ...
55 views

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 ...
165 views

157 views

140 views

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 $z'$??
88 views

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 ...
203 views

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?
628 views

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.
20 views

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.
105 views

505 views

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 $x$. ...