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Simplifying x2 + -16x + -3200 = 0 Reorder the terms: -3200 + -16x + x2 = 0 Solving -3200 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + -16x + 3200 + x2 = 0 + 3200 Reorder the terms: -3200 + 3200 + -16x + x2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + -16x + x2 = 0 + 3200 -16x + x2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 -16x + x2 = 3200 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 = 3200 + 64 Reorder the terms: 64 + -16x + x2 = 3200 + 64 Combine like terms: 3200 + 64 = 3264 64 + -16x + x2 = 3264 Factor a perfect square on the left side: (x + -8)(x + -8) = 3264 Calculate the square root of the right side: 57.131427428 Break this problem into two subproblems by setting (x + -8) equal to 57.131427428 and -57.131427428.Subproblem 1
x + -8 = 57.131427428 Simplifying x + -8 = 57.131427428 Reorder the terms: -8 + x = 57.131427428 Solving -8 + x = 57.131427428 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 = 57.131427428 + 8 Combine like terms: -8 + 8 = 0 0 + x = 57.131427428 + 8 x = 57.131427428 + 8 Combine like terms: 57.131427428 + 8 = 65.131427428 x = 65.131427428 Simplifying x = 65.131427428Subproblem 2
x + -8 = -57.131427428 Simplifying x + -8 = -57.131427428 Reorder the terms: -8 + x = -57.131427428 Solving -8 + x = -57.131427428 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 = -57.131427428 + 8 Combine like terms: -8 + 8 = 0 0 + x = -57.131427428 + 8 x = -57.131427428 + 8 Combine like terms: -57.131427428 + 8 = -49.131427428 x = -49.131427428 Simplifying x = -49.131427428Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.131427428, -49.131427428}
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