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Simplifying (80 + -4x)(20 + 8x) = 80 Multiply (80 + -4x) * (20 + 8x) (80(20 + 8x) + -4x * (20 + 8x)) = 80 ((20 * 80 + 8x * 80) + -4x * (20 + 8x)) = 80 ((1600 + 640x) + -4x * (20 + 8x)) = 80 (1600 + 640x + (20 * -4x + 8x * -4x)) = 80 (1600 + 640x + (-80x + -32x2)) = 80 Combine like terms: 640x + -80x = 560x (1600 + 560x + -32x2) = 80 Solving 1600 + 560x + -32x2 = 80 Solving for variable 'x'. Reorder the terms: 1600 + -80 + 560x + -32x2 = 80 + -80 Combine like terms: 1600 + -80 = 1520 1520 + 560x + -32x2 = 80 + -80 Combine like terms: 80 + -80 = 0 1520 + 560x + -32x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(95 + 35x + -2x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(95 + 35x + -2x2)' equal to zero and attempt to solve: Simplifying 95 + 35x + -2x2 = 0 Solving 95 + 35x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -47.5 + -17.5x + x2 = 0 Move the constant term to the right: Add '47.5' to each side of the equation. -47.5 + -17.5x + 47.5 + x2 = 0 + 47.5 Reorder the terms: -47.5 + 47.5 + -17.5x + x2 = 0 + 47.5 Combine like terms: -47.5 + 47.5 = 0.0 0.0 + -17.5x + x2 = 0 + 47.5 -17.5x + x2 = 0 + 47.5 Combine like terms: 0 + 47.5 = 47.5 -17.5x + x2 = 47.5 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 47.5 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 47.5 + 76.5625 Combine like terms: 47.5 + 76.5625 = 124.0625 76.5625 + -17.5x + x2 = 124.0625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 124.0625 Calculate the square root of the right side: 11.138334705 Break this problem into two subproblems by setting (x + -8.75) equal to 11.138334705 and -11.138334705.Subproblem 1
x + -8.75 = 11.138334705 Simplifying x + -8.75 = 11.138334705 Reorder the terms: -8.75 + x = 11.138334705 Solving -8.75 + x = 11.138334705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 11.138334705 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 11.138334705 + 8.75 x = 11.138334705 + 8.75 Combine like terms: 11.138334705 + 8.75 = 19.888334705 x = 19.888334705 Simplifying x = 19.888334705Subproblem 2
x + -8.75 = -11.138334705 Simplifying x + -8.75 = -11.138334705 Reorder the terms: -8.75 + x = -11.138334705 Solving -8.75 + x = -11.138334705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -11.138334705 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -11.138334705 + 8.75 x = -11.138334705 + 8.75 Combine like terms: -11.138334705 + 8.75 = -2.388334705 x = -2.388334705 Simplifying x = -2.388334705Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.888334705, -2.388334705}Solution
x = {19.888334705, -2.388334705}
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