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Simplifying (8x + 9) * x = 3 Reorder the terms: (9 + 8x) * x = 3 Reorder the terms for easier multiplication: x(9 + 8x) = 3 (9 * x + 8x * x) = 3 (9x + 8x2) = 3 Solving 9x + 8x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 9x + 8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 1.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 1.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 1.125x + x2 = 0 + 0.375 1.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 1.125x + x2 = 0.375 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 0.375 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.375 + 0.31640625 Combine like terms: 0.375 + 0.31640625 = 0.69140625 0.31640625 + 1.125x + x2 = 0.69140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.831508418 and -0.831508418.Subproblem 1
x + 0.5625 = 0.831508418 Simplifying x + 0.5625 = 0.831508418 Reorder the terms: 0.5625 + x = 0.831508418 Solving 0.5625 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 0.831508418 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.831508418 + -0.5625 x = 0.831508418 + -0.5625 Combine like terms: 0.831508418 + -0.5625 = 0.269008418 x = 0.269008418 Simplifying x = 0.269008418Subproblem 2
x + 0.5625 = -0.831508418 Simplifying x + 0.5625 = -0.831508418 Reorder the terms: 0.5625 + x = -0.831508418 Solving 0.5625 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -0.831508418 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.831508418 + -0.5625 x = -0.831508418 + -0.5625 Combine like terms: -0.831508418 + -0.5625 = -1.394008418 x = -1.394008418 Simplifying x = -1.394008418Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.269008418, -1.394008418}
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