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Simplifying 20x(8x + -2) = 74 Reorder the terms: 20x(-2 + 8x) = 74 (-2 * 20x + 8x * 20x) = 74 (-40x + 160x2) = 74 Solving -40x + 160x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + -40x + 160x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + -40x + 160x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-37 + -20x + 80x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-37 + -20x + 80x2)' equal to zero and attempt to solve: Simplifying -37 + -20x + 80x2 = 0 Solving -37 + -20x + 80x2 = 0 Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -0.4625 + -0.25x + x2 = 0.0 Move the constant term to the right: Add '0.4625' to each side of the equation. -0.4625 + -0.25x + 0.4625 + x2 = 0.0 + 0.4625 Reorder the terms: -0.4625 + 0.4625 + -0.25x + x2 = 0.0 + 0.4625 Combine like terms: -0.4625 + 0.4625 = 0.0000 0.0000 + -0.25x + x2 = 0.0 + 0.4625 -0.25x + x2 = 0.0 + 0.4625 Combine like terms: 0.0 + 0.4625 = 0.4625 -0.25x + x2 = 0.4625 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.4625 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.4625 + 0.015625 Combine like terms: 0.4625 + 0.015625 = 0.478125 0.015625 + -0.25x + x2 = 0.478125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.478125 Calculate the square root of the right side: 0.691465834 Break this problem into two subproblems by setting (x + -0.125) equal to 0.691465834 and -0.691465834.Subproblem 1
x + -0.125 = 0.691465834 Simplifying x + -0.125 = 0.691465834 Reorder the terms: -0.125 + x = 0.691465834 Solving -0.125 + x = 0.691465834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.691465834 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.691465834 + 0.125 x = 0.691465834 + 0.125 Combine like terms: 0.691465834 + 0.125 = 0.816465834 x = 0.816465834 Simplifying x = 0.816465834Subproblem 2
x + -0.125 = -0.691465834 Simplifying x + -0.125 = -0.691465834 Reorder the terms: -0.125 + x = -0.691465834 Solving -0.125 + x = -0.691465834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.691465834 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.691465834 + 0.125 x = -0.691465834 + 0.125 Combine like terms: -0.691465834 + 0.125 = -0.566465834 x = -0.566465834 Simplifying x = -0.566465834Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.816465834, -0.566465834}Solution
x = {0.816465834, -0.566465834}
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