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Simplifying -3x2 + 540x + -12 = 0 Reorder the terms: -12 + 540x + -3x2 = 0 Solving -12 + 540x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 180x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 180x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 180x + -1x2 = 0 Solving -4 + 180x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -180x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -180x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -180x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -180x + x2 = 0 + -4 -180x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -180x + x2 = -4 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -4 + 8100 Reorder the terms: 8100 + -180x + x2 = -4 + 8100 Combine like terms: -4 + 8100 = 8096 8100 + -180x + x2 = 8096 Factor a perfect square on the left side: (x + -90)(x + -90) = 8096 Calculate the square root of the right side: 89.977775034 Break this problem into two subproblems by setting (x + -90) equal to 89.977775034 and -89.977775034.Subproblem 1
x + -90 = 89.977775034 Simplifying x + -90 = 89.977775034 Reorder the terms: -90 + x = 89.977775034 Solving -90 + x = 89.977775034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.977775034 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.977775034 + 90 x = 89.977775034 + 90 Combine like terms: 89.977775034 + 90 = 179.977775034 x = 179.977775034 Simplifying x = 179.977775034Subproblem 2
x + -90 = -89.977775034 Simplifying x + -90 = -89.977775034 Reorder the terms: -90 + x = -89.977775034 Solving -90 + x = -89.977775034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.977775034 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.977775034 + 90 x = -89.977775034 + 90 Combine like terms: -89.977775034 + 90 = 0.022224966 x = 0.022224966 Simplifying x = 0.022224966Solution
The solution to the problem is based on the solutions from the subproblems. x = {179.977775034, 0.022224966}Solution
x = {179.977775034, 0.022224966}
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