Questions tagged [completing-the-square]

Questions on the algebraic operation of completing the square.

77 questions
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How are these related? completing the square vs. graphing a quadratic equation

While searching to learn about complex numbers on the Internet, I was referred also to quadratic equations. Several graphic examples showed how "completing the square" uses a quadratic equation to ...
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Completing square in hyperbolic equation

I tried completing the square for the following hyperbola: $x^2+y^2-3xy+2x+3y+2=0$ by sending $3xy+2$ to the other side and finally stuck here: $(x+1)^2 +2(y+\frac{3}{4})^2 = \frac{1}{8} -3xy$ I am ...
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Completing the Square with an A greater than 1

I need some assistance with a specific problem where the equation given is $-3x^2-3x+9=0$ I have divided everything by $-3$ to get $x^2+x-3=0$ Then I move the $3$ to the other side $x^2+x=3$ ...
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A question about a step in completing the square to prove the quadratic formula

$$\left(x+\dfrac{b}{2a}\right)^2 = \dfrac{-4ac+b^2}{4a^2}$$ goes to : $$\left(x+\dfrac{b}{2a}\right)^2 = \dfrac{b^2-4ac}{4a^2}$$ I don't understand how the signs changed in going from -4ac+b^2 to b^...
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I came across this polynomial $$x^2 - 2kxy + ky^2 +d; \, k>0$$ in some of my work and was wondering if there was a trick to coercing/factoring it into a polynomial of the form $$(x-x_0)^2-(y-y_0)... 2answers 91 views completing square for a circle In the following question: I don't understand how we can get from the original equation to the final equation using completing the square. Any thoughts as how to get to the final equation? 3answers 41 views Completing the square of x^2 - mx = 1 is not giving me the right answer. This is my attempt$$ \begin{align} x^2 - mx &= 1 \\ x^2 - mx - 1 &= 0 \\ \left(x^2 - mx + \frac{m^2}{4} - \frac{m^2}{4}\right) - 1 &= 0 \\ \left(x^2 - mx + \frac{m^2}{4}\...
I am running a bivariate regression with the formula $$\hat{Z} = b_0+b_1X+b_2Y+b_3X^2+b_4Y^2+b_5XY$$ I'm easily able to obtain the 6 coefficients this way. However, I want to reparameterize the ...