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Simplifying x2 + 32x + -128 = 0 Reorder the terms: -128 + 32x + x2 = 0 Solving -128 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 32x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 32x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 32x + x2 = 0 + 128 32x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 32x + x2 = 128 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 128 + 256 Reorder the terms: 256 + 32x + x2 = 128 + 256 Combine like terms: 128 + 256 = 384 256 + 32x + x2 = 384 Factor a perfect square on the left side: (x + 16)(x + 16) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (x + 16) equal to 19.595917942 and -19.595917942.Subproblem 1
x + 16 = 19.595917942 Simplifying x + 16 = 19.595917942 Reorder the terms: 16 + x = 19.595917942 Solving 16 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 19.595917942 + -16 Combine like terms: 16 + -16 = 0 0 + x = 19.595917942 + -16 x = 19.595917942 + -16 Combine like terms: 19.595917942 + -16 = 3.595917942 x = 3.595917942 Simplifying x = 3.595917942Subproblem 2
x + 16 = -19.595917942 Simplifying x + 16 = -19.595917942 Reorder the terms: 16 + x = -19.595917942 Solving 16 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -19.595917942 + -16 Combine like terms: 16 + -16 = 0 0 + x = -19.595917942 + -16 x = -19.595917942 + -16 Combine like terms: -19.595917942 + -16 = -35.595917942 x = -35.595917942 Simplifying x = -35.595917942Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.595917942, -35.595917942}
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