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Simplifying 2x(x + 52) = 90 Reorder the terms: 2x(52 + x) = 90 (52 * 2x + x * 2x) = 90 (104x + 2x2) = 90 Solving 104x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 104x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 104x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + 52x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + 52x + x2)' equal to zero and attempt to solve: Simplifying -45 + 52x + x2 = 0 Solving -45 + 52x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 52x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 52x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 52x + x2 = 0 + 45 52x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 52x + x2 = 45 The x term is 52x. Take half its coefficient (26). Square it (676) and add it to both sides. Add '676' to each side of the equation. 52x + 676 + x2 = 45 + 676 Reorder the terms: 676 + 52x + x2 = 45 + 676 Combine like terms: 45 + 676 = 721 676 + 52x + x2 = 721 Factor a perfect square on the left side: (x + 26)(x + 26) = 721 Calculate the square root of the right side: 26.851443164 Break this problem into two subproblems by setting (x + 26) equal to 26.851443164 and -26.851443164.Subproblem 1
x + 26 = 26.851443164 Simplifying x + 26 = 26.851443164 Reorder the terms: 26 + x = 26.851443164 Solving 26 + x = 26.851443164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = 26.851443164 + -26 Combine like terms: 26 + -26 = 0 0 + x = 26.851443164 + -26 x = 26.851443164 + -26 Combine like terms: 26.851443164 + -26 = 0.851443164 x = 0.851443164 Simplifying x = 0.851443164Subproblem 2
x + 26 = -26.851443164 Simplifying x + 26 = -26.851443164 Reorder the terms: 26 + x = -26.851443164 Solving 26 + x = -26.851443164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + x = -26.851443164 + -26 Combine like terms: 26 + -26 = 0 0 + x = -26.851443164 + -26 x = -26.851443164 + -26 Combine like terms: -26.851443164 + -26 = -52.851443164 x = -52.851443164 Simplifying x = -52.851443164Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.851443164, -52.851443164}Solution
x = {0.851443164, -52.851443164}
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