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Simplifying x2 + 61x + -24 = 0 Reorder the terms: -24 + 61x + x2 = 0 Solving -24 + 61x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 61x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 61x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 61x + x2 = 0 + 24 61x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 61x + x2 = 24 The x term is 61x. Take half its coefficient (30.5). Square it (930.25) and add it to both sides. Add '930.25' to each side of the equation. 61x + 930.25 + x2 = 24 + 930.25 Reorder the terms: 930.25 + 61x + x2 = 24 + 930.25 Combine like terms: 24 + 930.25 = 954.25 930.25 + 61x + x2 = 954.25 Factor a perfect square on the left side: (x + 30.5)(x + 30.5) = 954.25 Calculate the square root of the right side: 30.890937182 Break this problem into two subproblems by setting (x + 30.5) equal to 30.890937182 and -30.890937182.Subproblem 1
x + 30.5 = 30.890937182 Simplifying x + 30.5 = 30.890937182 Reorder the terms: 30.5 + x = 30.890937182 Solving 30.5 + x = 30.890937182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30.5' to each side of the equation. 30.5 + -30.5 + x = 30.890937182 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + x = 30.890937182 + -30.5 x = 30.890937182 + -30.5 Combine like terms: 30.890937182 + -30.5 = 0.390937182 x = 0.390937182 Simplifying x = 0.390937182Subproblem 2
x + 30.5 = -30.890937182 Simplifying x + 30.5 = -30.890937182 Reorder the terms: 30.5 + x = -30.890937182 Solving 30.5 + x = -30.890937182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30.5' to each side of the equation. 30.5 + -30.5 + x = -30.890937182 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + x = -30.890937182 + -30.5 x = -30.890937182 + -30.5 Combine like terms: -30.890937182 + -30.5 = -61.390937182 x = -61.390937182 Simplifying x = -61.390937182Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.390937182, -61.390937182}
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