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Simplifying x2 + -4x + -128 = 0 Reorder the terms: -128 + -4x + x2 = 0 Solving -128 + -4x + 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 + -4x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -4x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -4x + x2 = 0 + 128 -4x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -4x + x2 = 128 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 128 + 4 Reorder the terms: 4 + -4x + x2 = 128 + 4 Combine like terms: 128 + 4 = 132 4 + -4x + x2 = 132 Factor a perfect square on the left side: (x + -2)(x + -2) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -2) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -2 = 11.489125293 Simplifying x + -2 = 11.489125293 Reorder the terms: -2 + x = 11.489125293 Solving -2 + x = 11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.489125293 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.489125293 + 2 x = 11.489125293 + 2 Combine like terms: 11.489125293 + 2 = 13.489125293 x = 13.489125293 Simplifying x = 13.489125293Subproblem 2
x + -2 = -11.489125293 Simplifying x + -2 = -11.489125293 Reorder the terms: -2 + x = -11.489125293 Solving -2 + x = -11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.489125293 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.489125293 + 2 x = -11.489125293 + 2 Combine like terms: -11.489125293 + 2 = -9.489125293 x = -9.489125293 Simplifying x = -9.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.489125293, -9.489125293}
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