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Simplifying 5x + -88 + x(x + -65) = 8 Reorder the terms: 5x + -88 + x(-65 + x) = 8 5x + -88 + (-65 * x + x * x) = 8 5x + -88 + (-65x + x2) = 8 Reorder the terms: -88 + 5x + -65x + x2 = 8 Combine like terms: 5x + -65x = -60x -88 + -60x + x2 = 8 Solving -88 + -60x + x2 = 8 Solving for variable 'x'. Reorder the terms: -88 + -8 + -60x + x2 = 8 + -8 Combine like terms: -88 + -8 = -96 -96 + -60x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -96 + -60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -60x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -60x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -60x + x2 = 0 + 96 -60x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -60x + x2 = 96 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 96 + 900 Reorder the terms: 900 + -60x + x2 = 96 + 900 Combine like terms: 96 + 900 = 996 900 + -60x + x2 = 996 Factor a perfect square on the left side: (x + -30)(x + -30) = 996 Calculate the square root of the right side: 31.559467676 Break this problem into two subproblems by setting (x + -30) equal to 31.559467676 and -31.559467676.Subproblem 1
x + -30 = 31.559467676 Simplifying x + -30 = 31.559467676 Reorder the terms: -30 + x = 31.559467676 Solving -30 + x = 31.559467676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 31.559467676 + 30 Combine like terms: -30 + 30 = 0 0 + x = 31.559467676 + 30 x = 31.559467676 + 30 Combine like terms: 31.559467676 + 30 = 61.559467676 x = 61.559467676 Simplifying x = 61.559467676Subproblem 2
x + -30 = -31.559467676 Simplifying x + -30 = -31.559467676 Reorder the terms: -30 + x = -31.559467676 Solving -30 + x = -31.559467676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -31.559467676 + 30 Combine like terms: -30 + 30 = 0 0 + x = -31.559467676 + 30 x = -31.559467676 + 30 Combine like terms: -31.559467676 + 30 = -1.559467676 x = -1.559467676 Simplifying x = -1.559467676Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.559467676, -1.559467676}
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