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Simplifying 2x(x + 0.5) = 10 Reorder the terms: 2x(0.5 + x) = 10 (0.5 * 2x + x * 2x) = 10 (1x + 2x2) = 10 Solving 1x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 1x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 1x + 2x2 = 0 Factor a trinomial. (-5 + -2x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2.5, 2}
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