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Simplifying 10x2 + 3x + 9 = 13 Reorder the terms: 9 + 3x + 10x2 = 13 Solving 9 + 3x + 10x2 = 13 Solving for variable 'x'. Reorder the terms: 9 + -13 + 3x + 10x2 = 13 + -13 Combine like terms: 9 + -13 = -4 -4 + 3x + 10x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -4 + 3x + 10x2 = 0 Factor a trinomial. (-4 + -5x)(1 + -2x) = 0Subproblem 1
Set the factor '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8Subproblem 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 = {-0.8, 0.5}
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