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Simplifying 0 = x2 + 52x + 32 Reorder the terms: 0 = 32 + 52x + x2 Solving 0 = 32 + 52x + x2 Solving for variable 'x'. Combine like terms: 0 + -32 = -32 -32 + -52x + -1x2 = 32 + 52x + x2 + -32 + -52x + -1x2 Reorder the terms: -32 + -52x + -1x2 = 32 + -32 + 52x + -52x + x2 + -1x2 Combine like terms: 32 + -32 = 0 -32 + -52x + -1x2 = 0 + 52x + -52x + x2 + -1x2 -32 + -52x + -1x2 = 52x + -52x + x2 + -1x2 Combine like terms: 52x + -52x = 0 -32 + -52x + -1x2 = 0 + x2 + -1x2 -32 + -52x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + -52x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 52x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(32 + 52x + x2)' equal to zero and attempt to solve: Simplifying 32 + 52x + x2 = 0 Solving 32 + 52x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 52x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 52x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 52x + x2 = 0 + -32 52x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 52x + x2 = -32 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 = -32 + 676 Reorder the terms: 676 + 52x + x2 = -32 + 676 Combine like terms: -32 + 676 = 644 676 + 52x + x2 = 644 Factor a perfect square on the left side: (x + 26)(x + 26) = 644 Calculate the square root of the right side: 25.377155081 Break this problem into two subproblems by setting (x + 26) equal to 25.377155081 and -25.377155081.Subproblem 1
x + 26 = 25.377155081 Simplifying x + 26 = 25.377155081 Reorder the terms: 26 + x = 25.377155081 Solving 26 + x = 25.377155081 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 = 25.377155081 + -26 Combine like terms: 26 + -26 = 0 0 + x = 25.377155081 + -26 x = 25.377155081 + -26 Combine like terms: 25.377155081 + -26 = -0.622844919 x = -0.622844919 Simplifying x = -0.622844919Subproblem 2
x + 26 = -25.377155081 Simplifying x + 26 = -25.377155081 Reorder the terms: 26 + x = -25.377155081 Solving 26 + x = -25.377155081 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 = -25.377155081 + -26 Combine like terms: 26 + -26 = 0 0 + x = -25.377155081 + -26 x = -25.377155081 + -26 Combine like terms: -25.377155081 + -26 = -51.377155081 x = -51.377155081 Simplifying x = -51.377155081Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.622844919, -51.377155081}Solution
x = {-0.622844919, -51.377155081}
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