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Simplifying x2 + 24x + 58 = 0 Reorder the terms: 58 + 24x + x2 = 0 Solving 58 + 24x + x2 = 0 Solving for variable 'x'. 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 = 86 144 + 24x + x2 = 86 Factor a perfect square on the left side: (x + 12)(x + 12) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 12) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 12 = 9.273618495 Simplifying x + 12 = 9.273618495 Reorder the terms: 12 + x = 9.273618495 Solving 12 + x = 9.273618495 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 = 9.273618495 + -12 Combine like terms: 12 + -12 = 0 0 + x = 9.273618495 + -12 x = 9.273618495 + -12 Combine like terms: 9.273618495 + -12 = -2.726381505 x = -2.726381505 Simplifying x = -2.726381505Subproblem 2
x + 12 = -9.273618495 Simplifying x + 12 = -9.273618495 Reorder the terms: 12 + x = -9.273618495 Solving 12 + x = -9.273618495 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 = -9.273618495 + -12 Combine like terms: 12 + -12 = 0 0 + x = -9.273618495 + -12 x = -9.273618495 + -12 Combine like terms: -9.273618495 + -12 = -21.273618495 x = -21.273618495 Simplifying x = -21.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.726381505, -21.273618495}
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