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Simplifying 57 = 8x2 + 6x Reorder the terms: 57 = 6x + 8x2 Solving 57 = 6x + 8x2 Solving for variable 'x'. Reorder the terms: 57 + -6x + -8x2 = 6x + -6x + 8x2 + -8x2 Combine like terms: 6x + -6x = 0 57 + -6x + -8x2 = 0 + 8x2 + -8x2 57 + -6x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 57 + -6x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -7.125 + 0.75x + x2 = 0 Move the constant term to the right: Add '7.125' to each side of the equation. -7.125 + 0.75x + 7.125 + x2 = 0 + 7.125 Reorder the terms: -7.125 + 7.125 + 0.75x + x2 = 0 + 7.125 Combine like terms: -7.125 + 7.125 = 0.000 0.000 + 0.75x + x2 = 0 + 7.125 0.75x + x2 = 0 + 7.125 Combine like terms: 0 + 7.125 = 7.125 0.75x + x2 = 7.125 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 = 7.125 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 7.125 + 0.140625 Combine like terms: 7.125 + 0.140625 = 7.265625 0.140625 + 0.75x + x2 = 7.265625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 7.265625 Calculate the square root of the right side: 2.695482332 Break this problem into two subproblems by setting (x + 0.375) equal to 2.695482332 and -2.695482332.Subproblem 1
x + 0.375 = 2.695482332 Simplifying x + 0.375 = 2.695482332 Reorder the terms: 0.375 + x = 2.695482332 Solving 0.375 + x = 2.695482332 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 = 2.695482332 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.695482332 + -0.375 x = 2.695482332 + -0.375 Combine like terms: 2.695482332 + -0.375 = 2.320482332 x = 2.320482332 Simplifying x = 2.320482332Subproblem 2
x + 0.375 = -2.695482332 Simplifying x + 0.375 = -2.695482332 Reorder the terms: 0.375 + x = -2.695482332 Solving 0.375 + x = -2.695482332 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 = -2.695482332 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.695482332 + -0.375 x = -2.695482332 + -0.375 Combine like terms: -2.695482332 + -0.375 = -3.070482332 x = -3.070482332 Simplifying x = -3.070482332Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.320482332, -3.070482332}
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