SOLUTION: Hi, I am working on a quadratic equation: x^2 + 4x + 4 = 7. I'm not sure if I've arrived at the correct answer...I have x = 2(plus/minus) sq.rt. 7....am I correct in thinking

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Question 86765: Hi,
I am working on a quadratic equation: x^2 + 4x + 4 = 7.
I'm not sure if I've arrived at the correct answer...I have x = 2(plus/minus) sq.rt. 7....am I correct in thinking this is the final answer?
Thank you!
Found 2 solutions by Earlsdon, tutorcecilia:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are almost absolutely correct! The two in your answer should be negative.
Starting with:
x%5E2+%2B+4x+%2B+4+=+7 Subtract 7 from both sides to get your equation into the standard form:ax%5E2%2Bbx%2Bc+=+0
x%5E2%2B4x-3+=+0 Applying the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a you'll get:
x+=+%28-4%2B-sqrt%284%5E2-4%281%29%28-3%29%29%29%2F2%281%29 Simplifying this:
x+=+%28-4%2B-sqrt%2816-%28-12%29%29%29%2F2
x+=+%28-4%2B-sqrt%2828%29%29%2F2 Simplifying further:
x+=+%28-4%2B-sqrt%284%2A7%29%29%2F2
x+=+%28-4%2B-2%2Asqrt%287%29%29%2F2 This should show + or -
x+=+-2%2Bsqrt%287%29 or x+=+-2-sqrt%287%29

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 4x + 4 = 7
x^2 + 4x + 4-7 = 7-7
x^2 + 4x -3=0
.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
x+=+%28-4+%2B-+sqrt%28+4%5E2-%284%29%281%29%28-3%29+%29%29%2F%282%2A1%29+
.
x+=+%28%28-4+%2B-+sqrt%28+16%2B12%29+%29%29%2F%282%29+%29
.
x+=+%28%28-4+%2B-+sqrt%28+28%29+%29%29%2F%282%29+%29
.
x+=+%28%28-4+%2B-+2sqrt%287%29+%29%29%2F%282%29+%29
.
x+=+%28%282%29-2+%2B-+1sqrt%287%29+%29%29%2F%282%29+%29 [factor out a (2)
.
x+=+%28%281%29-2+%2B-+1sqrt%287%29+%29%29%2F%281%29+%29 [cancel out]
.
x+=+%28-2+%2B-+sqrt%287%29+%29%29+%29[this form is acceptable for the final answer, but be sure to check your answer]
.
check by plugging the x's back into the orginal formula and solving.
.
x+=+%28-2+%2B+sqrt%287%29+%29%29+%29
x= 0.64575
x^2 + 4x + 4 = 7
(0.64575)^2 + 4(0.64575) + 4 = 7
6.999 = 7 [close enough]
.
and
.
x+=+%28-2+-+sqrt%287%29+%29%29+%29
x=-4.6457
(-4.6457)^2 + 4(-4.6457) + 4 = 7
6.999 = 7 [also, close enough]
.