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Simplifying 3(x2 + 4) + 5 = -6(x2 + 2x) + 13 Reorder the terms: 3(4 + x2) + 5 = -6(x2 + 2x) + 13 (4 * 3 + x2 * 3) + 5 = -6(x2 + 2x) + 13 (12 + 3x2) + 5 = -6(x2 + 2x) + 13 Reorder the terms: 12 + 5 + 3x2 = -6(x2 + 2x) + 13 Combine like terms: 12 + 5 = 17 17 + 3x2 = -6(x2 + 2x) + 13 Reorder the terms: 17 + 3x2 = -6(2x + x2) + 13 17 + 3x2 = (2x * -6 + x2 * -6) + 13 17 + 3x2 = (-12x + -6x2) + 13 Reorder the terms: 17 + 3x2 = 13 + -12x + -6x2 Solving 17 + 3x2 = 13 + -12x + -6x2 Solving for variable 'x'. Reorder the terms: 17 + -13 + 12x + 3x2 + 6x2 = 13 + -12x + -6x2 + -13 + 12x + 6x2 Combine like terms: 17 + -13 = 4 4 + 12x + 3x2 + 6x2 = 13 + -12x + -6x2 + -13 + 12x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 4 + 12x + 9x2 = 13 + -12x + -6x2 + -13 + 12x + 6x2 Reorder the terms: 4 + 12x + 9x2 = 13 + -13 + -12x + 12x + -6x2 + 6x2 Combine like terms: 13 + -13 = 0 4 + 12x + 9x2 = 0 + -12x + 12x + -6x2 + 6x2 4 + 12x + 9x2 = -12x + 12x + -6x2 + 6x2 Combine like terms: -12x + 12x = 0 4 + 12x + 9x2 = 0 + -6x2 + 6x2 4 + 12x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 4 + 12x + 9x2 = 0 Factor a trinomial. (2 + 3x)(2 + 3x) = 0Subproblem 1
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-0.6666666667, -0.6666666667}
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