# Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Practice: 2

The solution set is ${x = \frac{3 + 1\sqrt11}{2}, x = \frac{3 - 1\sqrt11}{2}}$

#### Work Step by Step

$2x^2-6x=1$ Step-1 : Write the equation in standard form by subtracting 1 from both sides. $2x^2-6x-1=0$ Now, a = 2; b = -6; c = -1 The quadratic formula is: $x = \frac{-b ± \sqrt{b^2-4ac}}{2a}$ Step 2: Substitute in the quadratic formula and solve: $x = \frac{-(-6) ± \sqrt{(-6) ^2-(4 \times 2 \times -1)}}{2 \times 2}$ $x = \frac{6 ± \sqrt{36-(-8)}}{4}$ $x = \frac{6 ± \sqrt{36+8}}{4}$ $x = \frac{6 ± \sqrt44}{4}$ $x = \frac{6 ± \sqrt{11\times 4}}{4}$ $x = \frac{6 ± 2\sqrt{11}}{4}$ $x = \frac{2(3 ± 1\sqrt11)}{2 \times 2}$ $x = \frac{3 ± 1\sqrt11}{2}$ The solution set is ${x = \frac{3 + 1\sqrt11}{2}, x = \frac{3 - 1\sqrt11}{2}}$

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