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Simplifying x2 + 16x + -224 = 0 Reorder the terms: -224 + 16x + x2 = 0 Solving -224 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 16x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 16x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 16x + x2 = 0 + 224 16x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 16x + x2 = 224 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 224 + 64 Reorder the terms: 64 + 16x + x2 = 224 + 64 Combine like terms: 224 + 64 = 288 64 + 16x + x2 = 288 Factor a perfect square on the left side: (x + 8)(x + 8) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + 8) equal to 16.970562748 and -16.970562748.Subproblem 1
x + 8 = 16.970562748 Simplifying x + 8 = 16.970562748 Reorder the terms: 8 + x = 16.970562748 Solving 8 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 16.970562748 + -8 Combine like terms: 8 + -8 = 0 0 + x = 16.970562748 + -8 x = 16.970562748 + -8 Combine like terms: 16.970562748 + -8 = 8.970562748 x = 8.970562748 Simplifying x = 8.970562748Subproblem 2
x + 8 = -16.970562748 Simplifying x + 8 = -16.970562748 Reorder the terms: 8 + x = -16.970562748 Solving 8 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -16.970562748 + -8 Combine like terms: 8 + -8 = 0 0 + x = -16.970562748 + -8 x = -16.970562748 + -8 Combine like terms: -16.970562748 + -8 = -24.970562748 x = -24.970562748 Simplifying x = -24.970562748Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.970562748, -24.970562748}
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