(x^2)=(3x+10)

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Solution for (x^2)=(3x+10) equation:


Simplifying
(x2) = (3x + 10)
x2 = (3x + 10)

Reorder the terms:
x2 = (10 + 3x)

Remove parenthesis around (10 + 3x)
x2 = 10 + 3x

Solving
x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + -3x + x2 = 10 + 3x + -10 + -3x

Reorder the terms:
-10 + -3x + x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
-10 + -3x + x2 = 0 + 3x + -3x
-10 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + -3x + x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-2, 5}

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