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Simplifying x2 + -1x + -670 = 0 Reorder the terms: -670 + -1x + x2 = 0 Solving -670 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '670' to each side of the equation. -670 + -1x + 670 + x2 = 0 + 670 Reorder the terms: -670 + 670 + -1x + x2 = 0 + 670 Combine like terms: -670 + 670 = 0 0 + -1x + x2 = 0 + 670 -1x + x2 = 0 + 670 Combine like terms: 0 + 670 = 670 -1x + x2 = 670 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 = 670 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 670 + 0.25 Combine like terms: 670 + 0.25 = 670.25 0.25 + -1x + x2 = 670.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 670.25 Calculate the square root of the right side: 25.889186932 Break this problem into two subproblems by setting (x + -0.5) equal to 25.889186932 and -25.889186932.Subproblem 1
x + -0.5 = 25.889186932 Simplifying x + -0.5 = 25.889186932 Reorder the terms: -0.5 + x = 25.889186932 Solving -0.5 + x = 25.889186932 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 = 25.889186932 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 25.889186932 + 0.5 x = 25.889186932 + 0.5 Combine like terms: 25.889186932 + 0.5 = 26.389186932 x = 26.389186932 Simplifying x = 26.389186932Subproblem 2
x + -0.5 = -25.889186932 Simplifying x + -0.5 = -25.889186932 Reorder the terms: -0.5 + x = -25.889186932 Solving -0.5 + x = -25.889186932 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 = -25.889186932 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -25.889186932 + 0.5 x = -25.889186932 + 0.5 Combine like terms: -25.889186932 + 0.5 = -25.389186932 x = -25.389186932 Simplifying x = -25.389186932Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.389186932, -25.389186932}
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