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Simplifying 32x2 + -1x = 54 Reorder the terms: -1x + 32x2 = 54 Solving -1x + 32x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -1x + 32x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -1x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.6875 + -0.03125x + x2 = 0 Move the constant term to the right: Add '1.6875' to each side of the equation. -1.6875 + -0.03125x + 1.6875 + x2 = 0 + 1.6875 Reorder the terms: -1.6875 + 1.6875 + -0.03125x + x2 = 0 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + -0.03125x + x2 = 0 + 1.6875 -0.03125x + x2 = 0 + 1.6875 Combine like terms: 0 + 1.6875 = 1.6875 -0.03125x + x2 = 1.6875 The x term is -0.03125x. Take half its coefficient (-0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. -0.03125x + 0.000244140625 + x2 = 1.6875 + 0.000244140625 Reorder the terms: 0.000244140625 + -0.03125x + x2 = 1.6875 + 0.000244140625 Combine like terms: 1.6875 + 0.000244140625 = 1.687744140625 0.000244140625 + -0.03125x + x2 = 1.687744140625 Factor a perfect square on the left side: (x + -0.015625)(x + -0.015625) = 1.687744140625 Calculate the square root of the right side: 1.299132072 Break this problem into two subproblems by setting (x + -0.015625) equal to 1.299132072 and -1.299132072.Subproblem 1
x + -0.015625 = 1.299132072 Simplifying x + -0.015625 = 1.299132072 Reorder the terms: -0.015625 + x = 1.299132072 Solving -0.015625 + x = 1.299132072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = 1.299132072 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = 1.299132072 + 0.015625 x = 1.299132072 + 0.015625 Combine like terms: 1.299132072 + 0.015625 = 1.314757072 x = 1.314757072 Simplifying x = 1.314757072Subproblem 2
x + -0.015625 = -1.299132072 Simplifying x + -0.015625 = -1.299132072 Reorder the terms: -0.015625 + x = -1.299132072 Solving -0.015625 + x = -1.299132072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = -1.299132072 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = -1.299132072 + 0.015625 x = -1.299132072 + 0.015625 Combine like terms: -1.299132072 + 0.015625 = -1.283507072 x = -1.283507072 Simplifying x = -1.283507072Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.314757072, -1.283507072}
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