502,550 views
15 votes
15 votes
Solve the following quadratic equation by completing the square: x² + 12x = 15

User Mittens
by
2.7k points

1 Answer

20 votes
20 votes
Answer:

x = -1.14 or -13.14

Explanations:

The given equation is:


x^2+12x\text{ = 15}

Find the half of 12, and add the square to both sides of the equation.

That is add 6² to both sides


x^2+12x\text{ + 6}^(2)\text{ = 15 + 6}^(2)
\begin{gathered} (x+6)^2\text{ = 15 + 3}6 \\ (x+6)^2\text{ = 51} \\ \end{gathered}

Find the square root of both sides:


\begin{gathered} \sqrt[]{(x+6)^2_{}}=\pm\sqrt[]{51} \\ \text{x + 6 = }\pm\sqrt[]{51} \\ x\text{ = -6 }\pm\sqrt[]{51} \\ \text{x = }-6\pm7.14 \\ x\text{ = -6+7.14 = }1.14 \\ x\text{ = -6 - 7.14} \\ \text{x = -13.14} \end{gathered}

x = -1.14 or -13.14

User Bob Kusik
by
2.7k points
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