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Simplifying 4(x2) + -116x + 96 = 0 Reorder the terms: 96 + -116x + 4x2 = 0 Solving 96 + -116x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -29x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -29x + x2)' equal to zero and attempt to solve: Simplifying 24 + -29x + x2 = 0 Solving 24 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -29x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -29x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -29x + x2 = 0 + -24 -29x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -29x + x2 = -24 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -24 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -24 + 210.25 Combine like terms: -24 + 210.25 = 186.25 210.25 + -29x + x2 = 186.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + -14.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + -14.5 = 13.647344064 Simplifying x + -14.5 = 13.647344064 Reorder the terms: -14.5 + x = 13.647344064 Solving -14.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.647344064 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.647344064 + 14.5 x = 13.647344064 + 14.5 Combine like terms: 13.647344064 + 14.5 = 28.147344064 x = 28.147344064 Simplifying x = 28.147344064Subproblem 2
x + -14.5 = -13.647344064 Simplifying x + -14.5 = -13.647344064 Reorder the terms: -14.5 + x = -13.647344064 Solving -14.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.647344064 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.647344064 + 14.5 x = -13.647344064 + 14.5 Combine like terms: -13.647344064 + 14.5 = 0.852655936 x = 0.852655936 Simplifying x = 0.852655936Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.147344064, 0.852655936}Solution
x = {28.147344064, 0.852655936}
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