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Simplifying 8X2 + 6X + -7 = 0 Reorder the terms: -7 + 6X + 8X2 = 0 Solving -7 + 6X + 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'. -0.875 + 0.75X + X2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.75X + 0.875 + X2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.75X + X2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.75X + X2 = 0 + 0.875 0.75X + X2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.75X + X2 = 0.875 The X term is 0.75X. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75X + 0.140625 + X2 = 0.875 + 0.140625 Reorder the terms: 0.140625 + 0.75X + X2 = 0.875 + 0.140625 Combine like terms: 0.875 + 0.140625 = 1.015625 0.140625 + 0.75X + X2 = 1.015625 Factor a perfect square on the left side: (X + 0.375)(X + 0.375) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (X + 0.375) equal to 1.007782219 and -1.007782219.Subproblem 1
X + 0.375 = 1.007782219 Simplifying X + 0.375 = 1.007782219 Reorder the terms: 0.375 + X = 1.007782219 Solving 0.375 + X = 1.007782219 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + X = 1.007782219 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + X = 1.007782219 + -0.375 X = 1.007782219 + -0.375 Combine like terms: 1.007782219 + -0.375 = 0.632782219 X = 0.632782219 Simplifying X = 0.632782219Subproblem 2
X + 0.375 = -1.007782219 Simplifying X + 0.375 = -1.007782219 Reorder the terms: 0.375 + X = -1.007782219 Solving 0.375 + X = -1.007782219 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + X = -1.007782219 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + X = -1.007782219 + -0.375 X = -1.007782219 + -0.375 Combine like terms: -1.007782219 + -0.375 = -1.382782219 X = -1.382782219 Simplifying X = -1.382782219Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.632782219, -1.382782219}
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