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Simplifying 180 = 80 + x(4x + -80) Reorder the terms: 180 = 80 + x(-80 + 4x) 180 = 80 + (-80 * x + 4x * x) 180 = 80 + (-80x + 4x2) Solving 180 = 80 + -80x + 4x2 Solving for variable 'x'. Combine like terms: 180 + -80 = 100 100 + 80x + -4x2 = 80 + -80x + 4x2 + -80 + 80x + -4x2 Reorder the terms: 100 + 80x + -4x2 = 80 + -80 + -80x + 80x + 4x2 + -4x2 Combine like terms: 80 + -80 = 0 100 + 80x + -4x2 = 0 + -80x + 80x + 4x2 + -4x2 100 + 80x + -4x2 = -80x + 80x + 4x2 + -4x2 Combine like terms: -80x + 80x = 0 100 + 80x + -4x2 = 0 + 4x2 + -4x2 100 + 80x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 100 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying 25 + 20x + -1x2 = 0 Solving 25 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -20x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -20x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -20x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -20x + x2 = 0 + 25 -20x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -20x + x2 = 25 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 25 + 100 Reorder the terms: 100 + -20x + x2 = 25 + 100 Combine like terms: 25 + 100 = 125 100 + -20x + x2 = 125 Factor a perfect square on the left side: (x + -10)(x + -10) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -10) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -10 = 11.180339887 Simplifying x + -10 = 11.180339887 Reorder the terms: -10 + x = 11.180339887 Solving -10 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 11.180339887 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.180339887 + 10 x = 11.180339887 + 10 Combine like terms: 11.180339887 + 10 = 21.180339887 x = 21.180339887 Simplifying x = 21.180339887Subproblem 2
x + -10 = -11.180339887 Simplifying x + -10 = -11.180339887 Reorder the terms: -10 + x = -11.180339887 Solving -10 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -11.180339887 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.180339887 + 10 x = -11.180339887 + 10 Combine like terms: -11.180339887 + 10 = -1.180339887 x = -1.180339887 Simplifying x = -1.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.180339887, -1.180339887}Solution
x = {21.180339887, -1.180339887}
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