x^2-20=3x+50

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Solution for x^2-20=3x+50 equation:


Simplifying
x2 + -20 = 3x + 50

Reorder the terms:
-20 + x2 = 3x + 50

Reorder the terms:
-20 + x2 = 50 + 3x

Solving
-20 + x2 = 50 + 3x

Solving for variable 'x'.

Reorder the terms:
-20 + -50 + -3x + x2 = 50 + 3x + -50 + -3x

Combine like terms: -20 + -50 = -70
-70 + -3x + x2 = 50 + 3x + -50 + -3x

Reorder the terms:
-70 + -3x + x2 = 50 + -50 + 3x + -3x

Combine like terms: 50 + -50 = 0
-70 + -3x + x2 = 0 + 3x + -3x
-70 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-70 + -3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-7, 10}

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