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Simplifying x(x + -5) = x + 41 Reorder the terms: x(-5 + x) = x + 41 (-5 * x + x * x) = x + 41 (-5x + x2) = x + 41 Reorder the terms: -5x + x2 = 41 + x Solving -5x + x2 = 41 + x Solving for variable 'x'. Reorder the terms: -41 + -5x + -1x + x2 = 41 + x + -41 + -1x Combine like terms: -5x + -1x = -6x -41 + -6x + x2 = 41 + x + -41 + -1x Reorder the terms: -41 + -6x + x2 = 41 + -41 + x + -1x Combine like terms: 41 + -41 = 0 -41 + -6x + x2 = 0 + x + -1x -41 + -6x + x2 = x + -1x Combine like terms: x + -1x = 0 -41 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -6x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -6x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -6x + x2 = 0 + 41 -6x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -6x + x2 = 41 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 41 + 9 Reorder the terms: 9 + -6x + x2 = 41 + 9 Combine like terms: 41 + 9 = 50 9 + -6x + x2 = 50 Factor a perfect square on the left side: (x + -3)(x + -3) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -3) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -3 = 7.071067812 Simplifying x + -3 = 7.071067812 Reorder the terms: -3 + x = 7.071067812 Solving -3 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 7.071067812 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.071067812 + 3 x = 7.071067812 + 3 Combine like terms: 7.071067812 + 3 = 10.071067812 x = 10.071067812 Simplifying x = 10.071067812Subproblem 2
x + -3 = -7.071067812 Simplifying x + -3 = -7.071067812 Reorder the terms: -3 + x = -7.071067812 Solving -3 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -7.071067812 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.071067812 + 3 x = -7.071067812 + 3 Combine like terms: -7.071067812 + 3 = -4.071067812 x = -4.071067812 Simplifying x = -4.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.071067812, -4.071067812}
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