[tex]\sf~x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Our equation is in the form of [tex]\sf~ax^2+bx+c[/tex]
So in this case:
[tex]\sf~a=1[/tex]
[tex]\sf~b=7[/tex]
[tex]\sf~c=8[/tex]
[tex]\sf~x=\dfrac{-7\pm\sqrt{7^2-4(1)(8)}}{2(1)}[/tex]
Simplify exponent and the denominator:
[tex]\sf~x=\dfrac{-7\pm\sqrt{49-4(1)(8)}}{2}[/tex]
Multiply:
[tex]\sf~x=\dfrac{-7\pm\sqrt{49-32}}{2}[/tex]
Subtract:
[tex]\sf~x=\dfrac{-7\pm\sqrt{17}}{2}[/tex]
Simplify the square root:
[tex]\sf~x\approx\dfrac{-7\pm4.12310563}{2}[/tex]
Now this breaks into two equations.
[tex]\sf~x\approx\dfrac{-7+4.12310563}{2}[/tex]
and
[tex]\sf~x\approx\dfrac{-7-4.12310563}{2}[/tex]
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[tex]\sf~x\approx\dfrac{-7+4.12310563}{2}[/tex]
Add:
[tex]\sf~x\approx\dfrac{-2.87689437}{2}[/tex]
Divide:
[tex]\sf~x\approx-1.43844719[/tex]
Round to the nearest tenth:
[tex]\sf~x\approx\boxed{\sf-1.44}[/tex]
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[tex]\sf~x\approx\dfrac{-7-4.12310563}{2}[/tex]
Subtract:
[tex]\sf~x\approx\dfrac{-11.1231056}{2}[/tex]
Divide:
[tex]\sf~x\approx-5.5615528[/tex]
Round to the nearest tenth:
[tex]\sf~x\approx\boxed{\sf-5.56}[/tex]
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Your answers were correct.
