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Simplifying (x2) + 24x + -215 = 0 x2 + 24x + -215 = 0 Reorder the terms: -215 + 24x + x2 = 0 Solving -215 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '215' to each side of the equation. -215 + 24x + 215 + x2 = 0 + 215 Reorder the terms: -215 + 215 + 24x + x2 = 0 + 215 Combine like terms: -215 + 215 = 0 0 + 24x + x2 = 0 + 215 24x + x2 = 0 + 215 Combine like terms: 0 + 215 = 215 24x + x2 = 215 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 = 215 + 144 Reorder the terms: 144 + 24x + x2 = 215 + 144 Combine like terms: 215 + 144 = 359 144 + 24x + x2 = 359 Factor a perfect square on the left side: (x + 12)(x + 12) = 359 Calculate the square root of the right side: 18.947295321 Break this problem into two subproblems by setting (x + 12) equal to 18.947295321 and -18.947295321.Subproblem 1
x + 12 = 18.947295321 Simplifying x + 12 = 18.947295321 Reorder the terms: 12 + x = 18.947295321 Solving 12 + x = 18.947295321 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 = 18.947295321 + -12 Combine like terms: 12 + -12 = 0 0 + x = 18.947295321 + -12 x = 18.947295321 + -12 Combine like terms: 18.947295321 + -12 = 6.947295321 x = 6.947295321 Simplifying x = 6.947295321Subproblem 2
x + 12 = -18.947295321 Simplifying x + 12 = -18.947295321 Reorder the terms: 12 + x = -18.947295321 Solving 12 + x = -18.947295321 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 = -18.947295321 + -12 Combine like terms: 12 + -12 = 0 0 + x = -18.947295321 + -12 x = -18.947295321 + -12 Combine like terms: -18.947295321 + -12 = -30.947295321 x = -30.947295321 Simplifying x = -30.947295321Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.947295321, -30.947295321}
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