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Simplifying 95 = x2 + 20x + 65 Reorder the terms: 95 = 65 + 20x + x2 Solving 95 = 65 + 20x + x2 Solving for variable 'x'. Combine like terms: 95 + -65 = 30 30 + -20x + -1x2 = 65 + 20x + x2 + -65 + -20x + -1x2 Reorder the terms: 30 + -20x + -1x2 = 65 + -65 + 20x + -20x + x2 + -1x2 Combine like terms: 65 + -65 = 0 30 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 30 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 30 + -20x + -1x2 = 0 + x2 + -1x2 30 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 20x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 20x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 20x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 20x + x2 = 0 + 30 20x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 20x + x2 = 30 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 30 + 100 Reorder the terms: 100 + 20x + x2 = 30 + 100 Combine like terms: 30 + 100 = 130 100 + 20x + x2 = 130 Factor a perfect square on the left side: (x + 10)(x + 10) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 10) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 10 = 11.401754251 Simplifying x + 10 = 11.401754251 Reorder the terms: 10 + x = 11.401754251 Solving 10 + x = 11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.401754251 + -10 x = 11.401754251 + -10 Combine like terms: 11.401754251 + -10 = 1.401754251 x = 1.401754251 Simplifying x = 1.401754251Subproblem 2
x + 10 = -11.401754251 Simplifying x + 10 = -11.401754251 Reorder the terms: 10 + x = -11.401754251 Solving 10 + x = -11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.401754251 + -10 x = -11.401754251 + -10 Combine like terms: -11.401754251 + -10 = -21.401754251 x = -21.401754251 Simplifying x = -21.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.401754251, -21.401754251}
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