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Simplifying 4x2 + 26x = 72 Reorder the terms: 26x + 4x2 = 72 Solving 26x + 4x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + 26x + 4x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 26x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying -36 + 13x + 2x2 = 0 Solving -36 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 6.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 6.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 6.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6.5x + x2 = 0 + 18 6.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 6.5x + x2 = 18 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 18 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 18 + 10.5625 Combine like terms: 18 + 10.5625 = 28.5625 10.5625 + 6.5x + x2 = 28.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (x + 3.25) equal to 5.344389582 and -5.344389582.Subproblem 1
x + 3.25 = 5.344389582 Simplifying x + 3.25 = 5.344389582 Reorder the terms: 3.25 + x = 5.344389582 Solving 3.25 + x = 5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.344389582 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.344389582 + -3.25 x = 5.344389582 + -3.25 Combine like terms: 5.344389582 + -3.25 = 2.094389582 x = 2.094389582 Simplifying x = 2.094389582Subproblem 2
x + 3.25 = -5.344389582 Simplifying x + 3.25 = -5.344389582 Reorder the terms: 3.25 + x = -5.344389582 Solving 3.25 + x = -5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.344389582 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.344389582 + -3.25 x = -5.344389582 + -3.25 Combine like terms: -5.344389582 + -3.25 = -8.594389582 x = -8.594389582 Simplifying x = -8.594389582Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.094389582, -8.594389582}Solution
x = {2.094389582, -8.594389582}
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