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Simplifying 8x2 + 24 = -6x2 + 37x Reorder the terms: 24 + 8x2 = -6x2 + 37x Reorder the terms: 24 + 8x2 = 37x + -6x2 Solving 24 + 8x2 = 37x + -6x2 Solving for variable 'x'. Reorder the terms: 24 + -37x + 8x2 + 6x2 = 37x + -6x2 + -37x + 6x2 Combine like terms: 8x2 + 6x2 = 14x2 24 + -37x + 14x2 = 37x + -6x2 + -37x + 6x2 Reorder the terms: 24 + -37x + 14x2 = 37x + -37x + -6x2 + 6x2 Combine like terms: 37x + -37x = 0 24 + -37x + 14x2 = 0 + -6x2 + 6x2 24 + -37x + 14x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 24 + -37x + 14x2 = 0 Factor a trinomial. (8 + -7x)(3 + -2x) = 0Subproblem 1
Set the factor '(8 + -7x)' equal to zero and attempt to solve: Simplifying 8 + -7x = 0 Solving 8 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7x = 0 + -8 -7x = 0 + -8 Combine like terms: 0 + -8 = -8 -7x = -8 Divide each side by '-7'. x = 1.142857143 Simplifying x = 1.142857143Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {1.142857143, 1.5}
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