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Simplifying 32x2 + 9x + -36 = 0 Reorder the terms: -36 + 9x + 32x2 = 0 Solving -36 + 9x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.125 + 0.28125x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.28125x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.28125x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.28125x + x2 = 0 + 1.125 0.28125x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.28125x + x2 = 1.125 The x term is 0.28125x. Take half its coefficient (0.140625). Square it (0.01977539063) and add it to both sides. Add '0.01977539063' to each side of the equation. 0.28125x + 0.01977539063 + x2 = 1.125 + 0.01977539063 Reorder the terms: 0.01977539063 + 0.28125x + x2 = 1.125 + 0.01977539063 Combine like terms: 1.125 + 0.01977539063 = 1.14477539063 0.01977539063 + 0.28125x + x2 = 1.14477539063 Factor a perfect square on the left side: (x + 0.140625)(x + 0.140625) = 1.14477539063 Calculate the square root of the right side: 1.06994177 Break this problem into two subproblems by setting (x + 0.140625) equal to 1.06994177 and -1.06994177.Subproblem 1
x + 0.140625 = 1.06994177 Simplifying x + 0.140625 = 1.06994177 Reorder the terms: 0.140625 + x = 1.06994177 Solving 0.140625 + x = 1.06994177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.140625' to each side of the equation. 0.140625 + -0.140625 + x = 1.06994177 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + x = 1.06994177 + -0.140625 x = 1.06994177 + -0.140625 Combine like terms: 1.06994177 + -0.140625 = 0.92931677 x = 0.92931677 Simplifying x = 0.92931677Subproblem 2
x + 0.140625 = -1.06994177 Simplifying x + 0.140625 = -1.06994177 Reorder the terms: 0.140625 + x = -1.06994177 Solving 0.140625 + x = -1.06994177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.140625' to each side of the equation. 0.140625 + -0.140625 + x = -1.06994177 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + x = -1.06994177 + -0.140625 x = -1.06994177 + -0.140625 Combine like terms: -1.06994177 + -0.140625 = -1.21056677 x = -1.21056677 Simplifying x = -1.21056677Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92931677, -1.21056677}
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