How do you solve x^2 +6x +8 =0x2+6x+8=0 using the quadratic formula?

2 Answers
Patrick N.
May 8, 2018

The answers are x=-2x=−2 and x=-4x=−4.

Explanation:

To start, the quadratic formula is x=(-bpmsqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a

In this problem, a = 1a=1 (as the x^2x2 term has no coefficient), b=6b=6, and c=8c=8.

Plug those values into the quadratic equation to get:

x=(-6pmsqrt(6^2-4(1)(8)))/(2(1))x=−6±√62−4(1)(8)2(1)

Multiply 2*12⋅1 on the bottom of the fraction:

x=(-6pmsqrt(6^2-4(1)(8)))/(2)x=−6±√62−4(1)(8)2

Square 66 and multiply 4*1*84⋅1⋅8 within the square root:

x=(-6pmsqrt(36-32))/(2)x=−6±√36−322

Subtract 36-3236−32 inside the root:

x=(-6pmsqrt(4))/(2)x=−6±√42

Solve for sqrt(4)√4

x=(-6pm2)/(2)x=−6±22

If the pm± is positive, you get

x=(-6+2)/(2)x=−6+22, which simplifies to x=(-4)/(2)x=−42, or color(red)(-2)−2

If the pm± is negative, you get

x=(-6-2)/(2)x=−6−22, which simplifies to x=(-8)/(2)x=−82, or color(red)(-4)−4

Vince G.
May 8, 2018

x = -2 or x = -4

Explanation:

The quadratic formula looks like
x = (-b +- sqrt(b^2 - 4ac))/(2a)x=−b±√b2−4ac2a

You have...
ax^2 + bx + c = 0ax2+bx+c=0
and your equation...
x^2 + 6x +8 = 0x2+6x+8=0

With that you can do...
x^2 +6x + 8 = 0x2+6x+8=0
a = 1a=1
b = 6b=6
c = 8c=8

Then you substitute what you have into the quadratic formula
When you do that you get...
x = (-(6) +- sqrt((6)^2 - 4(1)(8)))/(2(a))x=−(6)±√(6)2−4(1)(8)2(a)

The '+-±' means that your going to have 2 answers like x = this or that so, you can just solve the whole equation using '++' first then use '-−' next.

when you do that you'll get an answer of x = -2 or -4x=−2or−4

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