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Simplifying x2 + x + -140000 = 0 Reorder the terms: -140000 + x + x2 = 0 Solving -140000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '140000' to each side of the equation. -140000 + x + 140000 + x2 = 0 + 140000 Reorder the terms: -140000 + 140000 + x + x2 = 0 + 140000 Combine like terms: -140000 + 140000 = 0 0 + x + x2 = 0 + 140000 x + x2 = 0 + 140000 Combine like terms: 0 + 140000 = 140000 x + x2 = 140000 The x term is x. 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. x + 0.25 + x2 = 140000 + 0.25 Reorder the terms: 0.25 + x + x2 = 140000 + 0.25 Combine like terms: 140000 + 0.25 = 140000.25 0.25 + x + x2 = 140000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 140000.25 Calculate the square root of the right side: 374.166072754 Break this problem into two subproblems by setting (x + 0.5) equal to 374.166072754 and -374.166072754.Subproblem 1
x + 0.5 = 374.166072754 Simplifying x + 0.5 = 374.166072754 Reorder the terms: 0.5 + x = 374.166072754 Solving 0.5 + x = 374.166072754 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 = 374.166072754 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 374.166072754 + -0.5 x = 374.166072754 + -0.5 Combine like terms: 374.166072754 + -0.5 = 373.666072754 x = 373.666072754 Simplifying x = 373.666072754Subproblem 2
x + 0.5 = -374.166072754 Simplifying x + 0.5 = -374.166072754 Reorder the terms: 0.5 + x = -374.166072754 Solving 0.5 + x = -374.166072754 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 = -374.166072754 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -374.166072754 + -0.5 x = -374.166072754 + -0.5 Combine like terms: -374.166072754 + -0.5 = -374.666072754 x = -374.666072754 Simplifying x = -374.666072754Solution
The solution to the problem is based on the solutions from the subproblems. x = {373.666072754, -374.666072754}
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