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Simplifying x2 + 4x = 128 Reorder the terms: 4x + x2 = 128 Solving 4x + x2 = 128 Solving for variable 'x'. Reorder the terms: -128 + 4x + x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -128 + 4x + x2 = 0 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 = 9.489125293 x = 9.489125293 Simplifying x = 9.489125293Subproblem 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 = -13.489125293 x = -13.489125293 Simplifying x = -13.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.489125293, -13.489125293}
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