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Simplifying 7x2 + -14x + -88 = -5 Reorder the terms: -88 + -14x + 7x2 = -5 Solving -88 + -14x + 7x2 = -5 Solving for variable 'x'. Reorder the terms: -88 + 5 + -14x + 7x2 = -5 + 5 Combine like terms: -88 + 5 = -83 -83 + -14x + 7x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -83 + -14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -11.85714286 + -2x + x2 = 0 Move the constant term to the right: Add '11.85714286' to each side of the equation. -11.85714286 + -2x + 11.85714286 + x2 = 0 + 11.85714286 Reorder the terms: -11.85714286 + 11.85714286 + -2x + x2 = 0 + 11.85714286 Combine like terms: -11.85714286 + 11.85714286 = 0.00000000 0.00000000 + -2x + x2 = 0 + 11.85714286 -2x + x2 = 0 + 11.85714286 Combine like terms: 0 + 11.85714286 = 11.85714286 -2x + x2 = 11.85714286 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 11.85714286 + 1 Reorder the terms: 1 + -2x + x2 = 11.85714286 + 1 Combine like terms: 11.85714286 + 1 = 12.85714286 1 + -2x + x2 = 12.85714286 Factor a perfect square on the left side: (x + -1)(x + -1) = 12.85714286 Calculate the square root of the right side: 3.585685828 Break this problem into two subproblems by setting (x + -1) equal to 3.585685828 and -3.585685828.Subproblem 1
x + -1 = 3.585685828 Simplifying x + -1 = 3.585685828 Reorder the terms: -1 + x = 3.585685828 Solving -1 + x = 3.585685828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.585685828 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.585685828 + 1 x = 3.585685828 + 1 Combine like terms: 3.585685828 + 1 = 4.585685828 x = 4.585685828 Simplifying x = 4.585685828Subproblem 2
x + -1 = -3.585685828 Simplifying x + -1 = -3.585685828 Reorder the terms: -1 + x = -3.585685828 Solving -1 + x = -3.585685828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.585685828 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.585685828 + 1 x = -3.585685828 + 1 Combine like terms: -3.585685828 + 1 = -2.585685828 x = -2.585685828 Simplifying x = -2.585685828Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.585685828, -2.585685828}
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