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Simplifying x2 + -1x + -1x0 = 1715 Reorder the terms: -1 + -1x + x2 = 1715 Solving -1 + -1x + x2 = 1715 Solving for variable 'x'. Reorder the terms: -1 + -1715 + -1x + x2 = 1715 + -1715 Combine like terms: -1 + -1715 = -1716 -1716 + -1x + x2 = 1715 + -1715 Combine like terms: 1715 + -1715 = 0 -1716 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1716' to each side of the equation. -1716 + -1x + 1716 + x2 = 0 + 1716 Reorder the terms: -1716 + 1716 + -1x + x2 = 0 + 1716 Combine like terms: -1716 + 1716 = 0 0 + -1x + x2 = 0 + 1716 -1x + x2 = 0 + 1716 Combine like terms: 0 + 1716 = 1716 -1x + x2 = 1716 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 = 1716 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1716 + 0.25 Combine like terms: 1716 + 0.25 = 1716.25 0.25 + -1x + x2 = 1716.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1716.25 Calculate the square root of the right side: 41.427647773 Break this problem into two subproblems by setting (x + -0.5) equal to 41.427647773 and -41.427647773.Subproblem 1
x + -0.5 = 41.427647773 Simplifying x + -0.5 = 41.427647773 Reorder the terms: -0.5 + x = 41.427647773 Solving -0.5 + x = 41.427647773 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 = 41.427647773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 41.427647773 + 0.5 x = 41.427647773 + 0.5 Combine like terms: 41.427647773 + 0.5 = 41.927647773 x = 41.927647773 Simplifying x = 41.927647773Subproblem 2
x + -0.5 = -41.427647773 Simplifying x + -0.5 = -41.427647773 Reorder the terms: -0.5 + x = -41.427647773 Solving -0.5 + x = -41.427647773 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 = -41.427647773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -41.427647773 + 0.5 x = -41.427647773 + 0.5 Combine like terms: -41.427647773 + 0.5 = -40.927647773 x = -40.927647773 Simplifying x = -40.927647773Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.927647773, -40.927647773}
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