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Simplifying 4x2 + -76x + 26 = 0 Reorder the terms: 26 + -76x + 4x2 = 0 Solving 26 + -76x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -38x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -38x + 2x2)' equal to zero and attempt to solve: Simplifying 13 + -38x + 2x2 = 0 Solving 13 + -38x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -19x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -19x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -19x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -19x + x2 = 0 + -6.5 -19x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -19x + x2 = -6.5 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -6.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -6.5 + 90.25 Combine like terms: -6.5 + 90.25 = 83.75 90.25 + -19x + x2 = 83.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 83.75 Calculate the square root of the right side: 9.151502609 Break this problem into two subproblems by setting (x + -9.5) equal to 9.151502609 and -9.151502609.Subproblem 1
x + -9.5 = 9.151502609 Simplifying x + -9.5 = 9.151502609 Reorder the terms: -9.5 + x = 9.151502609 Solving -9.5 + x = 9.151502609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.151502609 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.151502609 + 9.5 x = 9.151502609 + 9.5 Combine like terms: 9.151502609 + 9.5 = 18.651502609 x = 18.651502609 Simplifying x = 18.651502609Subproblem 2
x + -9.5 = -9.151502609 Simplifying x + -9.5 = -9.151502609 Reorder the terms: -9.5 + x = -9.151502609 Solving -9.5 + x = -9.151502609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.151502609 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.151502609 + 9.5 x = -9.151502609 + 9.5 Combine like terms: -9.151502609 + 9.5 = 0.348497391 x = 0.348497391 Simplifying x = 0.348497391Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.651502609, 0.348497391}Solution
x = {18.651502609, 0.348497391}
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