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Simplifying (2x + -3)(4x + -8) = 5x2 Reorder the terms: (-3 + 2x)(4x + -8) = 5x2 Reorder the terms: (-3 + 2x)(-8 + 4x) = 5x2 Multiply (-3 + 2x) * (-8 + 4x) (-3(-8 + 4x) + 2x * (-8 + 4x)) = 5x2 ((-8 * -3 + 4x * -3) + 2x * (-8 + 4x)) = 5x2 ((24 + -12x) + 2x * (-8 + 4x)) = 5x2 (24 + -12x + (-8 * 2x + 4x * 2x)) = 5x2 (24 + -12x + (-16x + 8x2)) = 5x2 Combine like terms: -12x + -16x = -28x (24 + -28x + 8x2) = 5x2 Solving 24 + -28x + 8x2 = 5x2 Solving for variable 'x'. Combine like terms: 8x2 + -5x2 = 3x2 24 + -28x + 3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 24 + -28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -9.333333333x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -9.333333333x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9.333333333x + x2 = 0 + -8 -9.333333333x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -9.333333333x + x2 = -8 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = -8 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = -8 + 21.77777778 Combine like terms: -8 + 21.77777778 = 13.77777778 21.77777778 + -9.333333333x + x2 = 13.77777778 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 13.77777778 Calculate the square root of the right side: 3.711842909 Break this problem into two subproblems by setting (x + -4.666666667) equal to 3.711842909 and -3.711842909.Subproblem 1
x + -4.666666667 = 3.711842909 Simplifying x + -4.666666667 = 3.711842909 Reorder the terms: -4.666666667 + x = 3.711842909 Solving -4.666666667 + x = 3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 3.711842909 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 3.711842909 + 4.666666667 x = 3.711842909 + 4.666666667 Combine like terms: 3.711842909 + 4.666666667 = 8.378509576 x = 8.378509576 Simplifying x = 8.378509576Subproblem 2
x + -4.666666667 = -3.711842909 Simplifying x + -4.666666667 = -3.711842909 Reorder the terms: -4.666666667 + x = -3.711842909 Solving -4.666666667 + x = -3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -3.711842909 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -3.711842909 + 4.666666667 x = -3.711842909 + 4.666666667 Combine like terms: -3.711842909 + 4.666666667 = 0.954823758 x = 0.954823758 Simplifying x = 0.954823758Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.378509576, 0.954823758}
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