SOLUTION: I just forgot how to do the algebra in this equation: (x^2) --------- = 49 (.4-x)^2

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Question 349708: I just forgot how to do the algebra in this equation:
(x^2)
--------- = 49
(.4-x)^2
Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
I just forgot how to do the algebra in this equation:
(x^2)
--------- = 49
(.4-x)^2

x^2 = 49 * (.4 - x)^2 (multiplied both sides by (.4 - x)^2)
x^2 = 49 * (.4 - x) * (.4 - x) (expanded the (.4 - x)^2)
x^2 = 49 * (.4^2 - .4x - .4x + x^2) (used FOIL, First Outer Inner Last)
x^2 = 49 * (.16 - .8x + x^2) (simplified)
x^2 = 49 * .16 - 49 * .8x + 49x^2 (distributed the 49 across)
x^2 = 7.84 - 39.2x + 49x^2
-49x^2 + x^2 + 39.2x - 7.84 = 0 (brought terms together and when putting terms to opposite side of equal sign changed sign on the terms)
-48x^2 + 39.2x - 7.84 = 0 (simplified)
48x^2 - 39.2x + 7.84 = 0 (divided both sides by -1)

if you want to solve for x, use the quadratic formula

in this case, a = 48, b = -39.2, c = 7.84

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=31.3600000000004 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.466666666666667, 0.35. Here's your graph: