Questions: Solve the equation using the quadratic formula.
x^2+13x+8=0
The solution set is (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Separate answers as needed.)
Transcript text: Solve the equation using the quadratic formula.
\[
x^{2}+13 x+8=0
\]
The solution set is $\square$ (Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use inte separate answers as needed.)
Solution
Solve the quadratic equation x2+13x+8=0 using the quadratic formula.
Identify the coefficients
The quadratic equation is in the form ax2+bx+c=0, where:
a=1
b=13
c=8
Apply the quadratic formula
Write the quadratic formula
The quadratic formula is:
x=2a−b±b2−4ac
Substitute the coefficients into the formula
Substitute a=1, b=13, and c=8 into the formula:
x=2⋅1−13±132−4⋅1⋅8
Simplify under the square root
Calculate the discriminant:
b2−4ac=132−4⋅1⋅8=169−32=137
Write the final expression
Substitute the discriminant back into the formula:
x=2−13±137
Write the solution set
Express the solutions
The solutions to the equation are:
x=2−13+137andx=2−13−137