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Simplifying 4x2 + -52x + 58 = 0 Reorder the terms: 58 + -52x + 4x2 = 0 Solving 58 + -52x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(29 + -26x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + -26x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + -26x + 2x2 = 0 Solving 29 + -26x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + -13x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + -13x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + -13x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + -13x + x2 = 0 + -14.5 -13x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 -13x + x2 = -14.5 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -14.5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -14.5 + 42.25 Combine like terms: -14.5 + 42.25 = 27.75 42.25 + -13x + x2 = 27.75 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 27.75 Calculate the square root of the right side: 5.267826876 Break this problem into two subproblems by setting (x + -6.5) equal to 5.267826876 and -5.267826876.Subproblem 1
x + -6.5 = 5.267826876 Simplifying x + -6.5 = 5.267826876 Reorder the terms: -6.5 + x = 5.267826876 Solving -6.5 + x = 5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.267826876 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.267826876 + 6.5 x = 5.267826876 + 6.5 Combine like terms: 5.267826876 + 6.5 = 11.767826876 x = 11.767826876 Simplifying x = 11.767826876Subproblem 2
x + -6.5 = -5.267826876 Simplifying x + -6.5 = -5.267826876 Reorder the terms: -6.5 + x = -5.267826876 Solving -6.5 + x = -5.267826876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.267826876 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.267826876 + 6.5 x = -5.267826876 + 6.5 Combine like terms: -5.267826876 + 6.5 = 1.232173124 x = 1.232173124 Simplifying x = 1.232173124Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.767826876, 1.232173124}Solution
x = {11.767826876, 1.232173124}
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