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Simplifying 3x + 4x * 8x = 9 Reorder the terms for easier multiplication: 3x + 4 * 8x * x = 9 Multiply 4 * 8 3x + 32x * x = 9 Multiply x * x 3x + 32x2 = 9 Solving 3x + 32x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 3x + 32x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 3x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.28125 + 0.09375x + x2 = 0 Move the constant term to the right: Add '0.28125' to each side of the equation. -0.28125 + 0.09375x + 0.28125 + x2 = 0 + 0.28125 Reorder the terms: -0.28125 + 0.28125 + 0.09375x + x2 = 0 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + 0.09375x + x2 = 0 + 0.28125 0.09375x + x2 = 0 + 0.28125 Combine like terms: 0 + 0.28125 = 0.28125 0.09375x + x2 = 0.28125 The x term is 0.09375x. Take half its coefficient (0.046875). Square it (0.002197265625) and add it to both sides. Add '0.002197265625' to each side of the equation. 0.09375x + 0.002197265625 + x2 = 0.28125 + 0.002197265625 Reorder the terms: 0.002197265625 + 0.09375x + x2 = 0.28125 + 0.002197265625 Combine like terms: 0.28125 + 0.002197265625 = 0.283447265625 0.002197265625 + 0.09375x + x2 = 0.283447265625 Factor a perfect square on the left side: (x + 0.046875)(x + 0.046875) = 0.283447265625 Calculate the square root of the right side: 0.532397657 Break this problem into two subproblems by setting (x + 0.046875) equal to 0.532397657 and -0.532397657.Subproblem 1
x + 0.046875 = 0.532397657 Simplifying x + 0.046875 = 0.532397657 Reorder the terms: 0.046875 + x = 0.532397657 Solving 0.046875 + x = 0.532397657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = 0.532397657 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = 0.532397657 + -0.046875 x = 0.532397657 + -0.046875 Combine like terms: 0.532397657 + -0.046875 = 0.485522657 x = 0.485522657 Simplifying x = 0.485522657Subproblem 2
x + 0.046875 = -0.532397657 Simplifying x + 0.046875 = -0.532397657 Reorder the terms: 0.046875 + x = -0.532397657 Solving 0.046875 + x = -0.532397657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = -0.532397657 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = -0.532397657 + -0.046875 x = -0.532397657 + -0.046875 Combine like terms: -0.532397657 + -0.046875 = -0.579272657 x = -0.579272657 Simplifying x = -0.579272657Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.485522657, -0.579272657}
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