Question

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.

Answer 1

`\sf~x=(-b\pm√(b^2-4ac))/(2a)`

Our equation is in the form of
`\sf~ax^2+bx+c`

So in this case:


`\sf~a=1`

`\sf~b=7`

`\sf~c=8`


`\sf~x=(-7\pm√(7^2-4(1)(8)))/(2(1))`

Simplify exponent and the denominator:


`\sf~x=(-7\pm√(49-4(1)(8)))/(2)`

Multiply:


`\sf~x=(-7\pm√(49-32))/(2)`

Subtract:


`\sf~x=(-7\pm√(17))/(2)`

Simplify the square root:


`\sf~x\approx(-7\pm4.12310563)/(2)`

Now this breaks into two equations.


`\sf~x\approx(-7+4.12310563)/(2)`

and


`\sf~x\approx(-7-4.12310563)/(2)`

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`\sf~x\approx(-7+4.12310563)/(2)`

Add:


`\sf~x\approx(-2.87689437)/(2)`

Divide:


`\sf~x\approx-1.43844719`

Round to the nearest tenth:


`\sf~x\approx\boxed{\sf-1.44}`

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`\sf~x\approx(-7-4.12310563)/(2)`

Subtract:


`\sf~x\approx(-11.1231056)/(2)`

Divide:


`\sf~x\approx-5.5615528`

Round to the nearest tenth:


`\sf~x\approx\boxed{\sf-5.56}`

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Your answers were correct.