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Exercises Roots and quadratic equations

Example 10.8 from Elementary Algebra, 10.1 Solve Quadratic Equations Using the Square Root Property

Solve Quadratic Equations Using the Square Root Property: example 10.8

Solve: ${(y - 7)}^{2} = 12$ .

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

${(y - 7)}^{2} = 12$

Use the Square Root Property. $y - 7 = \pm \sqrt{12}$

Simplify the radical. $y - 7 = \pm 2 \sqrt{3}$

Solve for y. $y = 7 \pm 2 \sqrt{3}$

Rewrite to show two solutions. $y = 7 + 2 \sqrt{3}, y = 7 - 2 \sqrt{3}$

Check.

Your turn

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

Solve: ${(a - 3)}^{2} = 18$ .

How did it go?

PreviousSolve Quadratic Equations Using the Square Root Property: example 10.7 Next Solve Quadratic Equations Using the Square Root Property: example 10.9

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 10.1, 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.