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Simplifying 0 = -180 + 100x + -4x2 Solving 0 = -180 + 100x + -4x2 Solving for variable 'x'. Combine like terms: 0 + 180 = 180 180 + -100x + 4x2 = -180 + 100x + -4x2 + 180 + -100x + 4x2 Reorder the terms: 180 + -100x + 4x2 = -180 + 180 + 100x + -100x + -4x2 + 4x2 Combine like terms: -180 + 180 = 0 180 + -100x + 4x2 = 0 + 100x + -100x + -4x2 + 4x2 180 + -100x + 4x2 = 100x + -100x + -4x2 + 4x2 Combine like terms: 100x + -100x = 0 180 + -100x + 4x2 = 0 + -4x2 + 4x2 180 + -100x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 180 + -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(45 + -25x + x2)' equal to zero and attempt to solve: Simplifying 45 + -25x + x2 = 0 Solving 45 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -25x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -25x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -25x + x2 = 0 + -45 -25x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -25x + x2 = -45 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -45 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -45 + 156.25 Combine like terms: -45 + 156.25 = 111.25 156.25 + -25x + x2 = 111.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + -12.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + -12.5 = 10.547511555 Simplifying x + -12.5 = 10.547511555 Reorder the terms: -12.5 + x = 10.547511555 Solving -12.5 + x = 10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.547511555 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.547511555 + 12.5 x = 10.547511555 + 12.5 Combine like terms: 10.547511555 + 12.5 = 23.047511555 x = 23.047511555 Simplifying x = 23.047511555Subproblem 2
x + -12.5 = -10.547511555 Simplifying x + -12.5 = -10.547511555 Reorder the terms: -12.5 + x = -10.547511555 Solving -12.5 + x = -10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.547511555 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.547511555 + 12.5 x = -10.547511555 + 12.5 Combine like terms: -10.547511555 + 12.5 = 1.952488445 x = 1.952488445 Simplifying x = 1.952488445Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.047511555, 1.952488445}Solution
x = {23.047511555, 1.952488445}
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