SOLUTION: Solve. x^2 7x 4 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Solve. x^2 7x 4 = 0       Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Mathway solves algebra homework problems with step-by-step help!


Question 88260: Solve. x^2 7x 4 = 0

Answer by jim_thompson5910(33401) About Me  (Show Source):
You can put this solution on YOUR website!
Now let's use the quadratic formula to solve for x:

Starting with the general quadratic


the general form of the quadratic equation is:


So lets solve x%5E2-7%2Ax-4=0 (notice a=1, b=-7, and c=-4)

x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=-4

x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29 Negate -7 to get 7

x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-4+%29%29%2F%282%2A1%29 Square -7 to get 49

x+=+%287+%2B-+sqrt%28+49%2B16+%29%29%2F%282%2A1%29 Multiply -4%2A-4%2A1 to get 16

x+=+%287+%2B-+sqrt%28+65+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)

x+=+%287+%2B-+sqrt%2865%29%29%2F%282%2A1%29 Simplify the square root

x+=+%287+%2B-+sqrt%2865%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%287+%2B+sqrt%2865%29%29%2F2 or x+=+%287+-+sqrt%2865%29%29%2F2

Which approximate to

x=7.53112887414927 or x=-0.531128874149275

So our solutions are:
x=7.53112887414927 or x=-0.531128874149275

Notice when we graph x%5E2-7%2Ax-4 we get:

when we use the root finder feature on a calculator, we find that x=7.53112887414927 and x=-0.531128874149275.So this verifies our answer