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Simplifying 3x + x(2 + 2) + 10 = 5(x2 + 2) + -3(x2 + -1) Combine like terms: 2 + 2 = 4 3x + x(4) + 10 = 5(x2 + 2) + -3(x2 + -1) Reorder the terms for easier multiplication: 3x + 4x + 10 = 5(x2 + 2) + -3(x2 + -1) Reorder the terms: 10 + 3x + 4x = 5(x2 + 2) + -3(x2 + -1) Combine like terms: 3x + 4x = 7x 10 + 7x = 5(x2 + 2) + -3(x2 + -1) Reorder the terms: 10 + 7x = 5(2 + x2) + -3(x2 + -1) 10 + 7x = (2 * 5 + x2 * 5) + -3(x2 + -1) 10 + 7x = (10 + 5x2) + -3(x2 + -1) Reorder the terms: 10 + 7x = 10 + 5x2 + -3(-1 + x2) 10 + 7x = 10 + 5x2 + (-1 * -3 + x2 * -3) 10 + 7x = 10 + 5x2 + (3 + -3x2) Reorder the terms: 10 + 7x = 10 + 3 + 5x2 + -3x2 Combine like terms: 10 + 3 = 13 10 + 7x = 13 + 5x2 + -3x2 Combine like terms: 5x2 + -3x2 = 2x2 10 + 7x = 13 + 2x2 Solving 10 + 7x = 13 + 2x2 Solving for variable 'x'. Reorder the terms: 10 + -13 + 7x + -2x2 = 13 + 2x2 + -13 + -2x2 Combine like terms: 10 + -13 = -3 -3 + 7x + -2x2 = 13 + 2x2 + -13 + -2x2 Reorder the terms: -3 + 7x + -2x2 = 13 + -13 + 2x2 + -2x2 Combine like terms: 13 + -13 = 0 -3 + 7x + -2x2 = 0 + 2x2 + -2x2 -3 + 7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 7x + -2x2 = 0 Factor a trinomial. (-3 + x)(1 + -2x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {3, 0.5}
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