kkaylight
contestada

Please help! I got −1.43844719 and −5.56155281

Use the quadratic formula to solve x2 + 7x + 8 = 0. Estimate irrational solutions to the nearest tenth.

Respuesta :

iGreen
[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.

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