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Simplifying x(x + -1) = 10 Reorder the terms: x(-1 + x) = 10 (-1 * x + x * x) = 10 (-1x + x2) = 10 Solving -1x + x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -1x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -1x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x + x2 = 0 + 10 -1x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1x + x2 = 10 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 = 10 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 10 + 0.25 Combine like terms: 10 + 0.25 = 10.25 0.25 + -1x + x2 = 10.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -0.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -0.5 = 3.201562119 Simplifying x + -0.5 = 3.201562119 Reorder the terms: -0.5 + x = 3.201562119 Solving -0.5 + x = 3.201562119 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 = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.201562119 + 0.5 x = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 x = 3.701562119 Simplifying x = 3.701562119Subproblem 2
x + -0.5 = -3.201562119 Simplifying x + -0.5 = -3.201562119 Reorder the terms: -0.5 + x = -3.201562119 Solving -0.5 + x = -3.201562119 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 = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.201562119 + 0.5 x = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 x = -2.701562119 Simplifying x = -2.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.701562119, -2.701562119}
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