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Simplifying 0 = 8x2 + 14x + -13 Reorder the terms: 0 = -13 + 14x + 8x2 Solving 0 = -13 + 14x + 8x2 Solving for variable 'x'. Combine like terms: 0 + 13 = 13 13 + -14x + -8x2 = -13 + 14x + 8x2 + 13 + -14x + -8x2 Reorder the terms: 13 + -14x + -8x2 = -13 + 13 + 14x + -14x + 8x2 + -8x2 Combine like terms: -13 + 13 = 0 13 + -14x + -8x2 = 0 + 14x + -14x + 8x2 + -8x2 13 + -14x + -8x2 = 14x + -14x + 8x2 + -8x2 Combine like terms: 14x + -14x = 0 13 + -14x + -8x2 = 0 + 8x2 + -8x2 13 + -14x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 13 + -14x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.625 + 1.75x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.75x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.75x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.75x + x2 = 0 + 1.625 1.75x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.75x + x2 = 1.625 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1.625 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1.625 + 0.765625 Combine like terms: 1.625 + 0.765625 = 2.390625 0.765625 + 1.75x + x2 = 2.390625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + 0.875) equal to 1.54616461 and -1.54616461.Subproblem 1
x + 0.875 = 1.54616461 Simplifying x + 0.875 = 1.54616461 Reorder the terms: 0.875 + x = 1.54616461 Solving 0.875 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.54616461 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.54616461 + -0.875 x = 1.54616461 + -0.875 Combine like terms: 1.54616461 + -0.875 = 0.67116461 x = 0.67116461 Simplifying x = 0.67116461Subproblem 2
x + 0.875 = -1.54616461 Simplifying x + 0.875 = -1.54616461 Reorder the terms: 0.875 + x = -1.54616461 Solving 0.875 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.54616461 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.54616461 + -0.875 x = -1.54616461 + -0.875 Combine like terms: -1.54616461 + -0.875 = -2.42116461 x = -2.42116461 Simplifying x = -2.42116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67116461, -2.42116461}
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