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Simplifying 4x2 + -23x + 53 = 5x + 8 Reorder the terms: 53 + -23x + 4x2 = 5x + 8 Reorder the terms: 53 + -23x + 4x2 = 8 + 5x Solving 53 + -23x + 4x2 = 8 + 5x Solving for variable 'x'. Reorder the terms: 53 + -8 + -23x + -5x + 4x2 = 8 + 5x + -8 + -5x Combine like terms: 53 + -8 = 45 45 + -23x + -5x + 4x2 = 8 + 5x + -8 + -5x Combine like terms: -23x + -5x = -28x 45 + -28x + 4x2 = 8 + 5x + -8 + -5x Reorder the terms: 45 + -28x + 4x2 = 8 + -8 + 5x + -5x Combine like terms: 8 + -8 = 0 45 + -28x + 4x2 = 0 + 5x + -5x 45 + -28x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 45 + -28x + 4x2 = 0 Factor a trinomial. (5 + -2x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {2.5, 4.5}
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