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siniylev [52]
10 months ago
10

Solve the following quadratic equation by completing the square: x² + 12x = 15

Mathematics
1 answer:
Lerok [7]10 months ago
3 0
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

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