SOLUTION: Solve by using the quadratic formula. x^2 = –7x + 12

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Question 83827: Solve by using the quadratic formula.
x^2 = –7x + 12
Found 2 solutions by josmiceli, Earlsdon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+-7x+%2B+12+
x%5E2+%2B+7x+-+12+=+0
This is now in the form
ax%5E2+%2B+bx+%2B+c+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 1
b = 7
c = -12
x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+
x+=+%28-7+%2B-+sqrt%2897%29%29%2F2+
The answers are:
x+=+%28-7+%2B+sqrt%2897%29%29+%2F+2
and
x+=+%28-7+-+sqrt%2897%29%29+%2F+2
You can check these answers by substituting for x in the
equation, but it's tough algebra. Instead, you can
evaluate sqrt%2897%29+=+9.849 and find the roots
x=+1.424 and x+=+-8.425
x%5E2+=+-7x+%2B+12+
%281.424%29%5E2+=+-7%2A%281.424%29+%2B+12
2.028+=+-+9.968+%2B+12
2.028+=+2.032 Not exact due to rounding-off errors,
but you get the idea

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
It would help if you were to put your equation into the standard form for quadratic equations:ax%5E2%2Bbx%2Bc+=+0
x%5E2+=+-7x%2B12 Add 7x to both sides.
x%5E2%2B7x+=+12 Now subtract 12 from both sides.
x%5E2%2B7x-12+=+0 So now you can see that a = 1, b = 7 and c = -12.
Applying the quadratic formula, you get:
x+=+%28-7%2B-sqrt%287%5E2-4%281%29%28-12%29%29%29%2F2%281%29 Simplify this.
x+=+%28-7%2B-sqrt%2849-%28-48%29%29%29%2F2
x+=+%28-7%2B-sqrt%2897%29%29%2F2
The solutions are:
x+=+%281%2F2%29%28-7%2Bsqrt%2897%29%29 and x+=+%281%2F2%29%28-7-sqrt%2897%29%29