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Simplifying x + 10 = x2 + -12x Reorder the terms: 10 + x = x2 + -12x Reorder the terms: 10 + x = -12x + x2 Solving 10 + x = -12x + x2 Solving for variable 'x'. Combine like terms: x + 12x = 13x 10 + 13x + -1x2 = -12x + x2 + 12x + -1x2 Reorder the terms: 10 + 13x + -1x2 = -12x + 12x + x2 + -1x2 Combine like terms: -12x + 12x = 0 10 + 13x + -1x2 = 0 + x2 + -1x2 10 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -13x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -13x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -13x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -13x + x2 = 0 + 10 -13x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -13x + x2 = 10 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 10 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 10 + 42.25 Combine like terms: 10 + 42.25 = 52.25 42.25 + -13x + x2 = 52.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -6.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -6.5 = 7.228416147 Simplifying x + -6.5 = 7.228416147 Reorder the terms: -6.5 + x = 7.228416147 Solving -6.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 7.228416147 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 7.228416147 + 6.5 x = 7.228416147 + 6.5 Combine like terms: 7.228416147 + 6.5 = 13.728416147 x = 13.728416147 Simplifying x = 13.728416147Subproblem 2
x + -6.5 = -7.228416147 Simplifying x + -6.5 = -7.228416147 Reorder the terms: -6.5 + x = -7.228416147 Solving -6.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -7.228416147 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -7.228416147 + 6.5 x = -7.228416147 + 6.5 Combine like terms: -7.228416147 + 6.5 = -0.728416147 x = -0.728416147 Simplifying x = -0.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.728416147, -0.728416147}
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