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Simplifying 35 = -4x2 + 24x Reorder the terms: 35 = 24x + -4x2 Solving 35 = 24x + -4x2 Solving for variable 'x'. Reorder the terms: 35 + -24x + 4x2 = 24x + -24x + -4x2 + 4x2 Combine like terms: 24x + -24x = 0 35 + -24x + 4x2 = 0 + -4x2 + 4x2 35 + -24x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 35 + -24x + 4x2 = 0 Factor a trinomial. (5 + -2x)(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {2.5, 3.5}
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