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Simplifying (2x2) + 234x + 4320 = 0 Reorder the terms: 4320 + 234x + (2x2) = 0 Solving 4320 + 234x + (2x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2160 + 117x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2160 + 117x + x2)' equal to zero and attempt to solve: Simplifying 2160 + 117x + x2 = 0 Solving 2160 + 117x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2160' to each side of the equation. 2160 + 117x + -2160 + x2 = 0 + -2160 Reorder the terms: 2160 + -2160 + 117x + x2 = 0 + -2160 Combine like terms: 2160 + -2160 = 0 0 + 117x + x2 = 0 + -2160 117x + x2 = 0 + -2160 Combine like terms: 0 + -2160 = -2160 117x + x2 = -2160 The x term is 117x. Take half its coefficient (58.5). Square it (3422.25) and add it to both sides. Add '3422.25' to each side of the equation. 117x + 3422.25 + x2 = -2160 + 3422.25 Reorder the terms: 3422.25 + 117x + x2 = -2160 + 3422.25 Combine like terms: -2160 + 3422.25 = 1262.25 3422.25 + 117x + x2 = 1262.25 Factor a perfect square on the left side: (x + 58.5)(x + 58.5) = 1262.25 Calculate the square root of the right side: 35.528157847 Break this problem into two subproblems by setting (x + 58.5) equal to 35.528157847 and -35.528157847.Subproblem 1
x + 58.5 = 35.528157847 Simplifying x + 58.5 = 35.528157847 Reorder the terms: 58.5 + x = 35.528157847 Solving 58.5 + x = 35.528157847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.5' to each side of the equation. 58.5 + -58.5 + x = 35.528157847 + -58.5 Combine like terms: 58.5 + -58.5 = 0.0 0.0 + x = 35.528157847 + -58.5 x = 35.528157847 + -58.5 Combine like terms: 35.528157847 + -58.5 = -22.971842153 x = -22.971842153 Simplifying x = -22.971842153Subproblem 2
x + 58.5 = -35.528157847 Simplifying x + 58.5 = -35.528157847 Reorder the terms: 58.5 + x = -35.528157847 Solving 58.5 + x = -35.528157847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-58.5' to each side of the equation. 58.5 + -58.5 + x = -35.528157847 + -58.5 Combine like terms: 58.5 + -58.5 = 0.0 0.0 + x = -35.528157847 + -58.5 x = -35.528157847 + -58.5 Combine like terms: -35.528157847 + -58.5 = -94.028157847 x = -94.028157847 Simplifying x = -94.028157847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-22.971842153, -94.028157847}Solution
x = {-22.971842153, -94.028157847}
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