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Simplifying 8x2 + -14x + -11 = 0 Reorder the terms: -11 + -14x + 8x2 = 0 Solving -11 + -14x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + -1.75x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -1.75x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -1.75x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -1.75x + x2 = 0 + 1.375 -1.75x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -1.75x + x2 = 1.375 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 = 1.375 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 1.375 + 0.765625 Combine like terms: 1.375 + 0.765625 = 2.140625 0.765625 + -1.75x + x2 = 2.140625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -0.875) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -0.875 = 1.463087489 Simplifying x + -0.875 = 1.463087489 Reorder the terms: -0.875 + x = 1.463087489 Solving -0.875 + x = 1.463087489 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 = 1.463087489 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.463087489 + 0.875 x = 1.463087489 + 0.875 Combine like terms: 1.463087489 + 0.875 = 2.338087489 x = 2.338087489 Simplifying x = 2.338087489Subproblem 2
x + -0.875 = -1.463087489 Simplifying x + -0.875 = -1.463087489 Reorder the terms: -0.875 + x = -1.463087489 Solving -0.875 + x = -1.463087489 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 = -1.463087489 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.463087489 + 0.875 x = -1.463087489 + 0.875 Combine like terms: -1.463087489 + 0.875 = -0.588087489 x = -0.588087489 Simplifying x = -0.588087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.338087489, -0.588087489}
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