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Simplifying x2 + 23x + 128 = 0 Reorder the terms: 128 + 23x + x2 = 0 Solving 128 + 23x + 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 + 23x + -128 + x2 = 0 + -128 Reorder the terms: 128 + -128 + 23x + x2 = 0 + -128 Combine like terms: 128 + -128 = 0 0 + 23x + x2 = 0 + -128 23x + x2 = 0 + -128 Combine like terms: 0 + -128 = -128 23x + x2 = -128 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = -128 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -128 + 132.25 Combine like terms: -128 + 132.25 = 4.25 132.25 + 23x + x2 = 4.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 11.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 11.5 = 2.061552813 Simplifying x + 11.5 = 2.061552813 Reorder the terms: 11.5 + x = 2.061552813 Solving 11.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 2.061552813 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 2.061552813 + -11.5 x = 2.061552813 + -11.5 Combine like terms: 2.061552813 + -11.5 = -9.438447187 x = -9.438447187 Simplifying x = -9.438447187Subproblem 2
x + 11.5 = -2.061552813 Simplifying x + 11.5 = -2.061552813 Reorder the terms: 11.5 + x = -2.061552813 Solving 11.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -2.061552813 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -2.061552813 + -11.5 x = -2.061552813 + -11.5 Combine like terms: -2.061552813 + -11.5 = -13.561552813 x = -13.561552813 Simplifying x = -13.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.438447187, -13.561552813}
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