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Simplifying x2 + -1x + -414 = 0 Reorder the terms: -414 + -1x + x2 = 0 Solving -414 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '414' to each side of the equation. -414 + -1x + 414 + x2 = 0 + 414 Reorder the terms: -414 + 414 + -1x + x2 = 0 + 414 Combine like terms: -414 + 414 = 0 0 + -1x + x2 = 0 + 414 -1x + x2 = 0 + 414 Combine like terms: 0 + 414 = 414 -1x + x2 = 414 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 = 414 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 414 + 0.25 Combine like terms: 414 + 0.25 = 414.25 0.25 + -1x + x2 = 414.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 414.25 Calculate the square root of the right side: 20.353132437 Break this problem into two subproblems by setting (x + -0.5) equal to 20.353132437 and -20.353132437.Subproblem 1
x + -0.5 = 20.353132437 Simplifying x + -0.5 = 20.353132437 Reorder the terms: -0.5 + x = 20.353132437 Solving -0.5 + x = 20.353132437 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 = 20.353132437 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 20.353132437 + 0.5 x = 20.353132437 + 0.5 Combine like terms: 20.353132437 + 0.5 = 20.853132437 x = 20.853132437 Simplifying x = 20.853132437Subproblem 2
x + -0.5 = -20.353132437 Simplifying x + -0.5 = -20.353132437 Reorder the terms: -0.5 + x = -20.353132437 Solving -0.5 + x = -20.353132437 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 = -20.353132437 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -20.353132437 + 0.5 x = -20.353132437 + 0.5 Combine like terms: -20.353132437 + 0.5 = -19.853132437 x = -19.853132437 Simplifying x = -19.853132437Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.853132437, -19.853132437}
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