x^2+x=5852

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Solution for x^2+x=5852 equation:


Simplifying
x2 + x = 5852

Reorder the terms:
x + x2 = 5852

Solving
x + x2 = 5852

Solving for variable 'x'.

Reorder the terms:
-5852 + x + x2 = 5852 + -5852

Combine like terms: 5852 + -5852 = 0
-5852 + x + x2 = 0

Factor a trinomial.
(-77 + -1x)(76 + -1x) = 0

Subproblem 1

Set the factor '(-77 + -1x)' equal to zero and attempt to solve: Simplifying -77 + -1x = 0 Solving -77 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '77' to each side of the equation. -77 + 77 + -1x = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -1x = 0 + 77 -1x = 0 + 77 Combine like terms: 0 + 77 = 77 -1x = 77 Divide each side by '-1'. x = -77 Simplifying x = -77

Subproblem 2

Set the factor '(76 + -1x)' equal to zero and attempt to solve: Simplifying 76 + -1x = 0 Solving 76 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-76' to each side of the equation. 76 + -76 + -1x = 0 + -76 Combine like terms: 76 + -76 = 0 0 + -1x = 0 + -76 -1x = 0 + -76 Combine like terms: 0 + -76 = -76 -1x = -76 Divide each side by '-1'. x = 76 Simplifying x = 76

Solution

x = {-77, 76}

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