SOLUTION: Find the exact value of x the whole line is 4x^2+3x+2 half the line is 7x-2 and the other half is 3x+7

Algebra ->  Length-and-distance -> SOLUTION: Find the exact value of x the whole line is 4x^2+3x+2 half the line is 7x-2 and the other half is 3x+7      Log On


   

Question 152786: Find the exact value of x
the whole line is 4x^2+3x+2
half the line is 7x-2 and the other half is 3x+7
Answer by mducky2(62) About Me  (Show Source):
You can put this solution on YOUR website!
Any time we only have one variable, we only need one equation to solve it. We know that the sum of the two halves of the line equals the whole line. Therefore:
highlight%287x-2+%2B+3x%2B7%29+=+4x%5E2+%2B+3x+%2B+2
10x%2B5+=+4x%5E2+%2B+3x+%2B+2

0+=+4x%5E2+-+7x+-+3

This can't be solved by factoring. Instead, we can use the quadratic formula.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

We know that in an equation ax2 + bx + c:
a+=+4
b+=+-7
c+=+-3

Let's plug in the numbers:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A4%2A%28-3%29+%29%29%2F%282%2A4%29+

x+=+%287+%2B-+sqrt%28+49-%28-48%29+%29%29%2F8+
x+=+%287+%2B-+sqrt%28highlight%2849-%28-48%29%29%29%29%2F8+
x+=+7+%2B-+sqrt%2897%29%2F8