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Simplifying x2 + -102x + -99 = 0 Reorder the terms: -99 + -102x + x2 = 0 Solving -99 + -102x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -102x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -102x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -102x + x2 = 0 + 99 -102x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -102x + x2 = 99 The x term is -102x. Take half its coefficient (-51). Square it (2601) and add it to both sides. Add '2601' to each side of the equation. -102x + 2601 + x2 = 99 + 2601 Reorder the terms: 2601 + -102x + x2 = 99 + 2601 Combine like terms: 99 + 2601 = 2700 2601 + -102x + x2 = 2700 Factor a perfect square on the left side: (x + -51)(x + -51) = 2700 Calculate the square root of the right side: 51.961524227 Break this problem into two subproblems by setting (x + -51) equal to 51.961524227 and -51.961524227.Subproblem 1
x + -51 = 51.961524227 Simplifying x + -51 = 51.961524227 Reorder the terms: -51 + x = 51.961524227 Solving -51 + x = 51.961524227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = 51.961524227 + 51 Combine like terms: -51 + 51 = 0 0 + x = 51.961524227 + 51 x = 51.961524227 + 51 Combine like terms: 51.961524227 + 51 = 102.961524227 x = 102.961524227 Simplifying x = 102.961524227Subproblem 2
x + -51 = -51.961524227 Simplifying x + -51 = -51.961524227 Reorder the terms: -51 + x = -51.961524227 Solving -51 + x = -51.961524227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '51' to each side of the equation. -51 + 51 + x = -51.961524227 + 51 Combine like terms: -51 + 51 = 0 0 + x = -51.961524227 + 51 x = -51.961524227 + 51 Combine like terms: -51.961524227 + 51 = -0.961524227 x = -0.961524227 Simplifying x = -0.961524227Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.961524227, -0.961524227}
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