4x^2+84x=400

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Solution for 4x^2+84x=400 equation:


Simplifying
4x2 + 84x = 400

Reorder the terms:
84x + 4x2 = 400

Solving
84x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 84x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 84x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-100 + 21x + x2) = 0

Factor a trinomial.
4((-25 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-25 + -1x)' equal to zero and attempt to solve: Simplifying -25 + -1x = 0 Solving -25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x = 0 + 25 -1x = 0 + 25 Combine like terms: 0 + 25 = 25 -1x = 25 Divide each side by '-1'. x = -25 Simplifying x = -25

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-25, 4}

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