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Exercises Equations and inequalities

Example 7 from Algebra and Trigonometry, 2.5 Quadratic Equations

Solving a Quadratic Equation Using the Square Root Property

Solve the quadratic equation: $4 x^{2} + 1 = 7.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, isolate the $x^{2}$ term. Then take the square root of both sides.

$\begin{matrix} 4 x^{2} + 1 & = & 7 \\ 4 x^{2} & = & 6 \\ x^{2} & = & \frac{6}{4} \\ x & = & \pm \frac{\sqrt{6}}{2} \end{matrix}$

The solutions are $\frac{\sqrt{6}}{2},$ and $- \frac{\sqrt{6}}{2} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the quadratic equation using the square root property: $3 {(x - 4)}^{2} = 15.$

How did it go?

PreviousSolving a Simple Quadratic Equation Using the Square Root Property Next Solving a Quadratic by Completing the Square

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.