McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Analyzing Functions with Successive Differences
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Exercise 45 Page 145

Rewrite the left hand side as a perfect square trinomial, then take the square root of each side.

3.1 and 10.9

Practice makes perfect
To solve a quadratic equation in the form x^2=n, take the square root of each side. For any number n≥ 0, if x^2=n, then x=±sqrt(n). Keeping this in mind, let's consider the given equation.
x^2-14x+49=15
(x-7)^2=15
sqrt((x-7)^2)=sqrt(15)
x-7=±sqrt(15)
x=7±sqrt(15)
Both x=7-sqrt(15), and x=7+sqrt(15) are solutions of the equation. Let's use a calculator to approximate our solutions. We see that rounded values are x=3.1, and x=10.9.