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Simplifying 4x2 + -46x + -76 = 0 Reorder the terms: -76 + -46x + 4x2 = 0 Solving -76 + -46x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-38 + -23x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-38 + -23x + 2x2)' equal to zero and attempt to solve: Simplifying -38 + -23x + 2x2 = 0 Solving -38 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + -11.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -11.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -11.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -11.5x + x2 = 0 + 19 -11.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -11.5x + x2 = 19 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 19 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 19 + 33.0625 Combine like terms: 19 + 33.0625 = 52.0625 33.0625 + -11.5x + x2 = 52.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 52.0625 Calculate the square root of the right side: 7.215434845 Break this problem into two subproblems by setting (x + -5.75) equal to 7.215434845 and -7.215434845.Subproblem 1
x + -5.75 = 7.215434845 Simplifying x + -5.75 = 7.215434845 Reorder the terms: -5.75 + x = 7.215434845 Solving -5.75 + x = 7.215434845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 7.215434845 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 7.215434845 + 5.75 x = 7.215434845 + 5.75 Combine like terms: 7.215434845 + 5.75 = 12.965434845 x = 12.965434845 Simplifying x = 12.965434845Subproblem 2
x + -5.75 = -7.215434845 Simplifying x + -5.75 = -7.215434845 Reorder the terms: -5.75 + x = -7.215434845 Solving -5.75 + x = -7.215434845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -7.215434845 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -7.215434845 + 5.75 x = -7.215434845 + 5.75 Combine like terms: -7.215434845 + 5.75 = -1.465434845 x = -1.465434845 Simplifying x = -1.465434845Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.965434845, -1.465434845}Solution
x = {12.965434845, -1.465434845}
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