Questions: Solve the following quadratic function by completing the square. y=x^2+2x-13 x=[?] pm sqrt

Solution Steps

The given quadratic function is:

\[ y = x^2 + 2x - 13 \]

To complete the square, we first focus on the quadratic and linear terms: \(x^2 + 2x\).

To complete the square, we need to add and subtract the square of half the coefficient of \(x\). The coefficient of \(x\) is 2, so half of it is 1, and its square is \(1^2 = 1\).

Add and subtract 1 inside the equation:

\[ y = (x^2 + 2x + 1) - 1 - 13 \]

This simplifies to:

\[ y = (x + 1)^2 - 14 \]

Now, we solve for \(x\) by setting \(y = 0\):

\[ 0 = (x + 1)^2 - 14 \]

Add 14 to both sides:

\[ (x + 1)^2 = 14 \]

Take the square root of both sides:

\[ x + 1 = \pm \sqrt{14} \]

Subtract 1 from both sides to solve for \(x\):

\[ x = -1 \pm \sqrt{14} \]

Final Answer