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Simplifying x2 + -1x + -10206 = 0 Reorder the terms: -10206 + -1x + x2 = 0 Solving -10206 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10206' to each side of the equation. -10206 + -1x + 10206 + x2 = 0 + 10206 Reorder the terms: -10206 + 10206 + -1x + x2 = 0 + 10206 Combine like terms: -10206 + 10206 = 0 0 + -1x + x2 = 0 + 10206 -1x + x2 = 0 + 10206 Combine like terms: 0 + 10206 = 10206 -1x + x2 = 10206 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 10206 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 10206 + 0.25 Combine like terms: 10206 + 0.25 = 10206.25 0.25 + -1x + x2 = 10206.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 10206.25 Calculate the square root of the right side: 101.025986756 Break this problem into two subproblems by setting (x + -0.5) equal to 101.025986756 and -101.025986756.Subproblem 1
x + -0.5 = 101.025986756 Simplifying x + -0.5 = 101.025986756 Reorder the terms: -0.5 + x = 101.025986756 Solving -0.5 + x = 101.025986756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 101.025986756 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 101.025986756 + 0.5 x = 101.025986756 + 0.5 Combine like terms: 101.025986756 + 0.5 = 101.525986756 x = 101.525986756 Simplifying x = 101.525986756Subproblem 2
x + -0.5 = -101.025986756 Simplifying x + -0.5 = -101.025986756 Reorder the terms: -0.5 + x = -101.025986756 Solving -0.5 + x = -101.025986756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -101.025986756 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -101.025986756 + 0.5 x = -101.025986756 + 0.5 Combine like terms: -101.025986756 + 0.5 = -100.525986756 x = -100.525986756 Simplifying x = -100.525986756Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.525986756, -100.525986756}
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