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Simplifying 9x + -4x(-8) * x = 15 Reorder the terms for easier multiplication: 9x + -4 * -8x * x = 15 Multiply -4 * -8 9x + 32x * x = 15 Multiply x * x 9x + 32x2 = 15 Solving 9x + 32x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 9x + 32x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 9x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.46875 + 0.28125x + x2 = 0 Move the constant term to the right: Add '0.46875' to each side of the equation. -0.46875 + 0.28125x + 0.46875 + x2 = 0 + 0.46875 Reorder the terms: -0.46875 + 0.46875 + 0.28125x + x2 = 0 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + 0.28125x + x2 = 0 + 0.46875 0.28125x + x2 = 0 + 0.46875 Combine like terms: 0 + 0.46875 = 0.46875 0.28125x + x2 = 0.46875 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 = 0.46875 + 0.01977539063 Reorder the terms: 0.01977539063 + 0.28125x + x2 = 0.46875 + 0.01977539063 Combine like terms: 0.46875 + 0.01977539063 = 0.48852539063 0.01977539063 + 0.28125x + x2 = 0.48852539063 Factor a perfect square on the left side: (x + 0.140625)(x + 0.140625) = 0.48852539063 Calculate the square root of the right side: 0.698945914 Break this problem into two subproblems by setting (x + 0.140625) equal to 0.698945914 and -0.698945914.Subproblem 1
x + 0.140625 = 0.698945914 Simplifying x + 0.140625 = 0.698945914 Reorder the terms: 0.140625 + x = 0.698945914 Solving 0.140625 + x = 0.698945914 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 = 0.698945914 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + x = 0.698945914 + -0.140625 x = 0.698945914 + -0.140625 Combine like terms: 0.698945914 + -0.140625 = 0.558320914 x = 0.558320914 Simplifying x = 0.558320914Subproblem 2
x + 0.140625 = -0.698945914 Simplifying x + 0.140625 = -0.698945914 Reorder the terms: 0.140625 + x = -0.698945914 Solving 0.140625 + x = -0.698945914 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 = -0.698945914 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + x = -0.698945914 + -0.140625 x = -0.698945914 + -0.140625 Combine like terms: -0.698945914 + -0.140625 = -0.839570914 x = -0.839570914 Simplifying x = -0.839570914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.558320914, -0.839570914}
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