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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 = 8104 8100 + -180x + x2 = 8104 Factor a perfect square on the left side: (x + -90)(x + -90) = 8104 Calculate the square root of the right side: 90.022219479 Break this problem into two subproblems by setting (x + -90) equal to 90.022219479 and -90.022219479.Subproblem 1
x + -90 = 90.022219479 Simplifying x + -90 = 90.022219479 Reorder the terms: -90 + x = 90.022219479 Solving -90 + x = 90.022219479 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 = 90.022219479 + 90 Combine like terms: -90 + 90 = 0 0 + x = 90.022219479 + 90 x = 90.022219479 + 90 Combine like terms: 90.022219479 + 90 = 180.022219479 x = 180.022219479 Simplifying x = 180.022219479Subproblem 2
x + -90 = -90.022219479 Simplifying x + -90 = -90.022219479 Reorder the terms: -90 + x = -90.022219479 Solving -90 + x = -90.022219479 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 = -90.022219479 + 90 Combine like terms: -90 + 90 = 0 0 + x = -90.022219479 + 90 x = -90.022219479 + 90 Combine like terms: -90.022219479 + 90 = -0.022219479 x = -0.022219479 Simplifying x = -0.022219479Solution
The solution to the problem is based on the solutions from the subproblems. x = {180.022219479, -0.022219479}Solution
x = {180.022219479, -0.022219479}
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