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Simplifying x(4x + 3) = 45 Reorder the terms: x(3 + 4x) = 45 (3 * x + 4x * x) = 45 (3x + 4x2) = 45 Solving 3x + 4x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 3x + 4x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 3x + 4x2 = 0 Factor a trinomial. (-15 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(-15 + -4x)' equal to zero and attempt to solve: Simplifying -15 + -4x = 0 Solving -15 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -4x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4x = 0 + 15 -4x = 0 + 15 Combine like terms: 0 + 15 = 15 -4x = 15 Divide each side by '-4'. x = -3.75 Simplifying x = -3.75Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-3.75, 3}
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