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Simplifying 8x2 = 7 + -3x Solving 8x2 = 7 + -3x Solving for variable 'x'. Reorder the terms: -7 + 3x + 8x2 = 7 + -3x + -7 + 3x Reorder the terms: -7 + 3x + 8x2 = 7 + -7 + -3x + 3x Combine like terms: 7 + -7 = 0 -7 + 3x + 8x2 = 0 + -3x + 3x -7 + 3x + 8x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -7 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 0.375x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.375x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.375x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.375x + x2 = 0 + 0.875 0.375x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.375x + x2 = 0.875 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 0.875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.875 + 0.03515625 Combine like terms: 0.875 + 0.03515625 = 0.91015625 0.03515625 + 0.375x + x2 = 0.91015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.954021095 and -0.954021095.Subproblem 1
x + 0.1875 = 0.954021095 Simplifying x + 0.1875 = 0.954021095 Reorder the terms: 0.1875 + x = 0.954021095 Solving 0.1875 + x = 0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.954021095 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.954021095 + -0.1875 x = 0.954021095 + -0.1875 Combine like terms: 0.954021095 + -0.1875 = 0.766521095 x = 0.766521095 Simplifying x = 0.766521095Subproblem 2
x + 0.1875 = -0.954021095 Simplifying x + 0.1875 = -0.954021095 Reorder the terms: 0.1875 + x = -0.954021095 Solving 0.1875 + x = -0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.954021095 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.954021095 + -0.1875 x = -0.954021095 + -0.1875 Combine like terms: -0.954021095 + -0.1875 = -1.141521095 x = -1.141521095 Simplifying x = -1.141521095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.766521095, -1.141521095}
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