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Chapter 6: Problem 79

Solve each equation by the method of your choice. \(2 x^{2}-9 x-3=9-9 x\)

Short Answer

Expert verified
The solutions to the equation are x = \(\sqrt{6}\) and x = -\(\sqrt{6}\).

Step by step solution

01

Simplify the equation

Combine similar terms and rewrite the equation in the simplified form. It gives \(2 x^{2}-9 x+9 x-3-9=0\), which simplifies to \(2x^2-12=0\).
02

Apply the Quadratic Formula

The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Substituting the values of a, b and c from the simplified quadratic equation \(a=2, b=0, c=-12\) we get \(x = \frac{-0 \pm \sqrt{(0)^2 - 4*2*(-12)}}{2*2}\).
03

Calculate the roots

Solving the formula will give two roots \(x = \frac{ \sqrt{(0)^2 - 4*2*(-12)}}{2*2}\) = \(\sqrt{6}\) and \(x = \frac{ -\sqrt{(0)^2 - 4*2*(-12)}}{2*2}\) = -\(\sqrt{6}\).

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