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Simplifying x2 + -5x + x2 + 10 + x2 + -8x + x + 520 + -17x = 540 Reorder the terms: 10 + 520 + -5x + -8x + x + -17x + x2 + x2 + x2 = 540 Combine like terms: 10 + 520 = 530 530 + -5x + -8x + x + -17x + x2 + x2 + x2 = 540 Combine like terms: -5x + -8x = -13x 530 + -13x + x + -17x + x2 + x2 + x2 = 540 Combine like terms: -13x + x = -12x 530 + -12x + -17x + x2 + x2 + x2 = 540 Combine like terms: -12x + -17x = -29x 530 + -29x + x2 + x2 + x2 = 540 Combine like terms: x2 + x2 = 2x2 530 + -29x + 2x2 + x2 = 540 Combine like terms: 2x2 + x2 = 3x2 530 + -29x + 3x2 = 540 Solving 530 + -29x + 3x2 = 540 Solving for variable 'x'. Reorder the terms: 530 + -540 + -29x + 3x2 = 540 + -540 Combine like terms: 530 + -540 = -10 -10 + -29x + 3x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -10 + -29x + 3x2 = 0 Factor a trinomial. (-1 + -3x)(10 + -1x) = 0Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 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 = 10Solution
x = {-0.3333333333, 10}
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