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Simplifying 4x(80 + -1x) = 180 (80 * 4x + -1x * 4x) = 180 (320x + -4x2) = 180 Solving 320x + -4x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 320x + -4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 320x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 80x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 80x + -1x2)' equal to zero and attempt to solve: Simplifying -45 + 80x + -1x2 = 0 Solving -45 + 80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 45 + -80x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -80x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -80x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -80x + x2 = 0 + -45 -80x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -80x + x2 = -45 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -45 + 1600 Reorder the terms: 1600 + -80x + x2 = -45 + 1600 Combine like terms: -45 + 1600 = 1555 1600 + -80x + x2 = 1555 Factor a perfect square on the left side: (x + -40)(x + -40) = 1555 Calculate the square root of the right side: 39.433488306 Break this problem into two subproblems by setting (x + -40) equal to 39.433488306 and -39.433488306.Subproblem 1
x + -40 = 39.433488306 Simplifying x + -40 = 39.433488306 Reorder the terms: -40 + x = 39.433488306 Solving -40 + x = 39.433488306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.433488306 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.433488306 + 40 x = 39.433488306 + 40 Combine like terms: 39.433488306 + 40 = 79.433488306 x = 79.433488306 Simplifying x = 79.433488306Subproblem 2
x + -40 = -39.433488306 Simplifying x + -40 = -39.433488306 Reorder the terms: -40 + x = -39.433488306 Solving -40 + x = -39.433488306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.433488306 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.433488306 + 40 x = -39.433488306 + 40 Combine like terms: -39.433488306 + 40 = 0.566511694 x = 0.566511694 Simplifying x = 0.566511694Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.433488306, 0.566511694}Solution
x = {79.433488306, 0.566511694}
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