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Simplifying 0 = 4x2 + 16x + -270 Reorder the terms: 0 = -270 + 16x + 4x2 Solving 0 = -270 + 16x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 270 = 270 270 + -16x + -4x2 = -270 + 16x + 4x2 + 270 + -16x + -4x2 Reorder the terms: 270 + -16x + -4x2 = -270 + 270 + 16x + -16x + 4x2 + -4x2 Combine like terms: -270 + 270 = 0 270 + -16x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2 270 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 270 + -16x + -4x2 = 0 + 4x2 + -4x2 270 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 270 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(135 + -8x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(135 + -8x + -2x2)' equal to zero and attempt to solve: Simplifying 135 + -8x + -2x2 = 0 Solving 135 + -8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -67.5 + 4x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + 4x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + 4x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + 4x + x2 = 0 + 67.5 4x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 4x + x2 = 67.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 67.5 + 4 Reorder the terms: 4 + 4x + x2 = 67.5 + 4 Combine like terms: 67.5 + 4 = 71.5 4 + 4x + x2 = 71.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 71.5 Calculate the square root of the right side: 8.455767263 Break this problem into two subproblems by setting (x + 2) equal to 8.455767263 and -8.455767263.Subproblem 1
x + 2 = 8.455767263 Simplifying x + 2 = 8.455767263 Reorder the terms: 2 + x = 8.455767263 Solving 2 + x = 8.455767263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.455767263 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.455767263 + -2 x = 8.455767263 + -2 Combine like terms: 8.455767263 + -2 = 6.455767263 x = 6.455767263 Simplifying x = 6.455767263Subproblem 2
x + 2 = -8.455767263 Simplifying x + 2 = -8.455767263 Reorder the terms: 2 + x = -8.455767263 Solving 2 + x = -8.455767263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.455767263 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.455767263 + -2 x = -8.455767263 + -2 Combine like terms: -8.455767263 + -2 = -10.455767263 x = -10.455767263 Simplifying x = -10.455767263Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.455767263, -10.455767263}Solution
x = {6.455767263, -10.455767263}
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