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Simplifying (2x + -5)(4x + 2) = 20 Reorder the terms: (-5 + 2x)(4x + 2) = 20 Reorder the terms: (-5 + 2x)(2 + 4x) = 20 Multiply (-5 + 2x) * (2 + 4x) (-5(2 + 4x) + 2x * (2 + 4x)) = 20 ((2 * -5 + 4x * -5) + 2x * (2 + 4x)) = 20 ((-10 + -20x) + 2x * (2 + 4x)) = 20 (-10 + -20x + (2 * 2x + 4x * 2x)) = 20 (-10 + -20x + (4x + 8x2)) = 20 Combine like terms: -20x + 4x = -16x (-10 + -16x + 8x2) = 20 Solving -10 + -16x + 8x2 = 20 Solving for variable 'x'. Reorder the terms: -10 + -20 + -16x + 8x2 = 20 + -20 Combine like terms: -10 + -20 = -30 -30 + -16x + 8x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -30 + -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + -8x + 4x2 = 0 Solving -15 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -2x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -2x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -2x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -2x + x2 = 0 + 3.75 -2x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -2x + x2 = 3.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.75 + 1 Reorder the terms: 1 + -2x + x2 = 3.75 + 1 Combine like terms: 3.75 + 1 = 4.75 1 + -2x + x2 = 4.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -1) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -1 = 2.179449472 Simplifying x + -1 = 2.179449472 Reorder the terms: -1 + x = 2.179449472 Solving -1 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.179449472 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.179449472 + 1 x = 2.179449472 + 1 Combine like terms: 2.179449472 + 1 = 3.179449472 x = 3.179449472 Simplifying x = 3.179449472Subproblem 2
x + -1 = -2.179449472 Simplifying x + -1 = -2.179449472 Reorder the terms: -1 + x = -2.179449472 Solving -1 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.179449472 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.179449472 + 1 x = -2.179449472 + 1 Combine like terms: -2.179449472 + 1 = -1.179449472 x = -1.179449472 Simplifying x = -1.179449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.179449472, -1.179449472}Solution
x = {3.179449472, -1.179449472}
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