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Completing the Square & the Quadratic Formula Practice
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Using the quadratic formula, find the solution to x2+6x+9=0
.(1 point)
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Answers
GPT-4o mini
To solve the quadratic equation \(x^2 + 6x + 9 = 0\) using the quadratic formula, we can recall that the quadratic formula is given by:
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
In this equation, \(a\), \(b\), and \(c\) are the coefficients from the general form of a quadratic equation \(ax^2 + bx + c = 0\). For the given equation \(x^2 + 6x + 9 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 6\)
- \(c = 9\)
Now, let's calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0
\]
Since the discriminant is zero, there will be exactly one real solution. Now, substituting the values of \(a\), \(b\), and the discriminant into the quadratic formula:
\[
x = \frac{{-6 \pm \sqrt{0}}}{2(1)}
\]
This simplifies to:
\[
x = \frac{{-6}}{2} = -3
\]
Thus, the solution to the equation \(x^2 + 6x + 9 = 0\) is:
\[
\boxed{-3}
\]
This indicates that \(-3\) is a double root of the equation.
\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]
In this equation, \(a\), \(b\), and \(c\) are the coefficients from the general form of a quadratic equation \(ax^2 + bx + c = 0\). For the given equation \(x^2 + 6x + 9 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 6\)
- \(c = 9\)
Now, let's calculate the discriminant \(b^2 - 4ac\):
\[
b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0
\]
Since the discriminant is zero, there will be exactly one real solution. Now, substituting the values of \(a\), \(b\), and the discriminant into the quadratic formula:
\[
x = \frac{{-6 \pm \sqrt{0}}}{2(1)}
\]
This simplifies to:
\[
x = \frac{{-6}}{2} = -3
\]
Thus, the solution to the equation \(x^2 + 6x + 9 = 0\) is:
\[
\boxed{-3}
\]
This indicates that \(-3\) is a double root of the equation.