x^2+4x+34=-9x+4

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Solution for x^2+4x+34=-9x+4 equation:


Simplifying
x2 + 4x + 34 = -9x + 4

Reorder the terms:
34 + 4x + x2 = -9x + 4

Reorder the terms:
34 + 4x + x2 = 4 + -9x

Solving
34 + 4x + x2 = 4 + -9x

Solving for variable 'x'.

Reorder the terms:
34 + -4 + 4x + 9x + x2 = 4 + -9x + -4 + 9x

Combine like terms: 34 + -4 = 30
30 + 4x + 9x + x2 = 4 + -9x + -4 + 9x

Combine like terms: 4x + 9x = 13x
30 + 13x + x2 = 4 + -9x + -4 + 9x

Reorder the terms:
30 + 13x + x2 = 4 + -4 + -9x + 9x

Combine like terms: 4 + -4 = 0
30 + 13x + x2 = 0 + -9x + 9x
30 + 13x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
30 + 13x + x2 = 0

Factor a trinomial.
(10 + x)(3 + x) = 0

Subproblem 1

Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-10, -3}

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