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Simplifying 8x * 8x + -18x + -5 = 0 Reorder the terms for easier multiplication: 8 * 8x * x + -18x + -5 = 0 Multiply 8 * 8 64x * x + -18x + -5 = 0 Multiply x * x 64x2 + -18x + -5 = 0 Reorder the terms: -5 + -18x + 64x2 = 0 Solving -5 + -18x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.078125 + -0.28125x + x2 = 0 Move the constant term to the right: Add '0.078125' to each side of the equation. -0.078125 + -0.28125x + 0.078125 + x2 = 0 + 0.078125 Reorder the terms: -0.078125 + 0.078125 + -0.28125x + x2 = 0 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + -0.28125x + x2 = 0 + 0.078125 -0.28125x + x2 = 0 + 0.078125 Combine like terms: 0 + 0.078125 = 0.078125 -0.28125x + x2 = 0.078125 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 = 0.078125 + 0.01977539063 Reorder the terms: 0.01977539063 + -0.28125x + x2 = 0.078125 + 0.01977539063 Combine like terms: 0.078125 + 0.01977539063 = 0.09790039063 0.01977539063 + -0.28125x + x2 = 0.09790039063 Factor a perfect square on the left side: (x + -0.140625)(x + -0.140625) = 0.09790039063 Calculate the square root of the right side: 0.312890381 Break this problem into two subproblems by setting (x + -0.140625) equal to 0.312890381 and -0.312890381.Subproblem 1
x + -0.140625 = 0.312890381 Simplifying x + -0.140625 = 0.312890381 Reorder the terms: -0.140625 + x = 0.312890381 Solving -0.140625 + x = 0.312890381 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 = 0.312890381 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + x = 0.312890381 + 0.140625 x = 0.312890381 + 0.140625 Combine like terms: 0.312890381 + 0.140625 = 0.453515381 x = 0.453515381 Simplifying x = 0.453515381Subproblem 2
x + -0.140625 = -0.312890381 Simplifying x + -0.140625 = -0.312890381 Reorder the terms: -0.140625 + x = -0.312890381 Solving -0.140625 + x = -0.312890381 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 = -0.312890381 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + x = -0.312890381 + 0.140625 x = -0.312890381 + 0.140625 Combine like terms: -0.312890381 + 0.140625 = -0.172265381 x = -0.172265381 Simplifying x = -0.172265381Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.453515381, -0.172265381}
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