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Simplifying x(x + 24) = 58 Reorder the terms: x(24 + x) = 58 (24 * x + x * x) = 58 (24x + x2) = 58 Solving 24x + x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + 24x + x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 24x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 24x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 24x + x2 = 0 + 58 24x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 24x + x2 = 58 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 58 + 144 Reorder the terms: 144 + 24x + x2 = 58 + 144 Combine like terms: 58 + 144 = 202 144 + 24x + x2 = 202 Factor a perfect square on the left side: (x + 12)(x + 12) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (x + 12) equal to 14.212670404 and -14.212670404.Subproblem 1
x + 12 = 14.212670404 Simplifying x + 12 = 14.212670404 Reorder the terms: 12 + x = 14.212670404 Solving 12 + x = 14.212670404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 14.212670404 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.212670404 + -12 x = 14.212670404 + -12 Combine like terms: 14.212670404 + -12 = 2.212670404 x = 2.212670404 Simplifying x = 2.212670404Subproblem 2
x + 12 = -14.212670404 Simplifying x + 12 = -14.212670404 Reorder the terms: 12 + x = -14.212670404 Solving 12 + x = -14.212670404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -14.212670404 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.212670404 + -12 x = -14.212670404 + -12 Combine like terms: -14.212670404 + -12 = -26.212670404 x = -26.212670404 Simplifying x = -26.212670404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.212670404, -26.212670404}
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