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Simplifying (x + -5)(x + -5) = 2x2 + -9 + 19 Reorder the terms: (-5 + x)(x + -5) = 2x2 + -9 + 19 Reorder the terms: (-5 + x)(-5 + x) = 2x2 + -9 + 19 Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x)) = 2x2 + -9 + 19 ((-5 * -5 + x * -5) + x(-5 + x)) = 2x2 + -9 + 19 ((25 + -5x) + x(-5 + x)) = 2x2 + -9 + 19 (25 + -5x + (-5 * x + x * x)) = 2x2 + -9 + 19 (25 + -5x + (-5x + x2)) = 2x2 + -9 + 19 Combine like terms: -5x + -5x = -10x (25 + -10x + x2) = 2x2 + -9 + 19 Reorder the terms: 25 + -10x + x2 = -9 + 19 + 2x2 Combine like terms: -9 + 19 = 10 25 + -10x + x2 = 10 + 2x2 Solving 25 + -10x + x2 = 10 + 2x2 Solving for variable 'x'. Reorder the terms: 25 + -10 + -10x + x2 + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: 25 + -10 = 15 15 + -10x + x2 + -2x2 = 10 + 2x2 + -10 + -2x2 Combine like terms: x2 + -2x2 = -1x2 15 + -10x + -1x2 = 10 + 2x2 + -10 + -2x2 Reorder the terms: 15 + -10x + -1x2 = 10 + -10 + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 15 + -10x + -1x2 = 0 + 2x2 + -2x2 15 + -10x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 10x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 10x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 10x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 10x + x2 = 0 + 15 10x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 10x + x2 = 15 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 15 + 25 Reorder the terms: 25 + 10x + x2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + 10x + x2 = 40 Factor a perfect square on the left side: (x + 5)(x + 5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 5) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 5 = 6.32455532 Simplifying x + 5 = 6.32455532 Reorder the terms: 5 + x = 6.32455532 Solving 5 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.32455532 + -5 x = 6.32455532 + -5 Combine like terms: 6.32455532 + -5 = 1.32455532 x = 1.32455532 Simplifying x = 1.32455532Subproblem 2
x + 5 = -6.32455532 Simplifying x + 5 = -6.32455532 Reorder the terms: 5 + x = -6.32455532 Solving 5 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.32455532 + -5 x = -6.32455532 + -5 Combine like terms: -6.32455532 + -5 = -11.32455532 x = -11.32455532 Simplifying x = -11.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.32455532, -11.32455532}
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