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In $9-26,$ solve each quadratic equation by completing the square. Express the answer in simplest radical form.$$x^{2}-6 x+2=0$$

$3+\sqrt{7}$ and $3-\sqrt{7}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 1

Real Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Missouri State University

Oregon State University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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In $9-26,$ solve each quad…

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Okay, This question wants us to solve the following quadratic. So we're going to use the method of completing the square which turns X squared plus B x plus e into Vertex for a Times X plus d squared plus e. And we said D is defined to be be over to a and e is defined as C minus B squared over for a So let's calculate these constants for our quadratic and Palladian. So we said that d is be over to a which in our example bees negative six days, one so d is negative three and then e is to minus B squared, which is 36 over for a So we get tu minus nine, which is negative seven. So are quadratic can now be it written in this reduced form as X minus three quantity squared minus seven is equal to zero, cause we just plugged into our complete the square form after we found D and E. So now we're gonna add seven double sides to get X minus. Three squared is equal to seven or X minus three is equal to plus or minus the square root of seven. So now we're gonna get to solutions we get one branch for X minus three equals positive Square seven and one branch for X minus three equals negative Route seven. So let's just add three double sides to get our solutions of X equals three plus Route seven and X equals three minus Route seven and those air answers.

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