6. Analyzing Functions with Successive Differences
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Rewrite the left hand side as a perfect square trinomial, then take the square root of each side.
3.1 and 10.9
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.
a^2+2ab+b^2=(a+b)^2
sqrt(LHS)=sqrt(RHS)
Calculate root
LHS+7=RHS+7
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.