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Simplifying (8x + -1)(5x) = 180 Reorder the terms: (-1 + 8x)(5x) = 180 Remove parenthesis around (5x) (-1 + 8x) * 5x = 180 Reorder the terms for easier multiplication: 5x(-1 + 8x) = 180 (-1 * 5x + 8x * 5x) = 180 (-5x + 40x2) = 180 Solving -5x + 40x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -5x + 40x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -5x + 40x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + -1x + 8x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying -36 + -1x + 8x2 = 0 Solving -36 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.125x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.125x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.125x + x2 = 0 + 4.5 -0.125x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.125x + x2 = 4.5 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 4.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 4.5 + 0.00390625 Combine like terms: 4.5 + 0.00390625 = 4.50390625 0.00390625 + -0.125x + x2 = 4.50390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 4.50390625 Calculate the square root of the right side: 2.122240856 Break this problem into two subproblems by setting (x + -0.0625) equal to 2.122240856 and -2.122240856.Subproblem 1
x + -0.0625 = 2.122240856 Simplifying x + -0.0625 = 2.122240856 Reorder the terms: -0.0625 + x = 2.122240856 Solving -0.0625 + x = 2.122240856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 2.122240856 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 2.122240856 + 0.0625 x = 2.122240856 + 0.0625 Combine like terms: 2.122240856 + 0.0625 = 2.184740856 x = 2.184740856 Simplifying x = 2.184740856Subproblem 2
x + -0.0625 = -2.122240856 Simplifying x + -0.0625 = -2.122240856 Reorder the terms: -0.0625 + x = -2.122240856 Solving -0.0625 + x = -2.122240856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -2.122240856 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -2.122240856 + 0.0625 x = -2.122240856 + 0.0625 Combine like terms: -2.122240856 + 0.0625 = -2.059740856 x = -2.059740856 Simplifying x = -2.059740856Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.184740856, -2.059740856}Solution
x = {2.184740856, -2.059740856}
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