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Chapter 6: Problem 80

Solve each equation by the method of your choice. \(3 x^{2}-6 x-3=12-6 x\)

Short Answer

Expert verified
The solutions of the equation are \(x=\sqrt{5}\) and \(x= - \sqrt{5}\).

Step by step solution

01

Rearrange the equation

Rearrange the equation \(3 x^{2}-6 x-3=12-6 x\) to bring all terms to one side, resulting in a standard form quadratic equation. The equation becomes \(3 x^{2}-6 x-3-(12-6 x)=0\), which simplifies to \(3x^{2}-15=0\).
02

Factor the quadratic equation

Next, factor the quadratic equation \(3x^{2}-15=0\). For this equation, it's very simple basically divide the equation by 3, then we get \(x^{2}-5=0\). Further, add 5 to both sides, then it becomes \(x^{2}=5\).
03

Solve the equation

The final step is to solve the equation \(x^{2}=5\). Given that the square root of 5 does not result in a whole number, the solutions are \(x=\sqrt{5}\) and \(x= - \sqrt{5}\).

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