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Simplifying x(8x + 9) = 5 Reorder the terms: x(9 + 8x) = 5 (9 * x + 8x * x) = 5 (9x + 8x2) = 5 Solving 9x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 9x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 1.125x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 1.125x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 1.125x + x2 = 0 + 0.625 1.125x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 1.125x + x2 = 0.625 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 = 0.625 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.625 + 0.31640625 Combine like terms: 0.625 + 0.31640625 = 0.94140625 0.31640625 + 1.125x + x2 = 0.94140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (x + 0.5625) equal to 0.970260919 and -0.970260919.Subproblem 1
x + 0.5625 = 0.970260919 Simplifying x + 0.5625 = 0.970260919 Reorder the terms: 0.5625 + x = 0.970260919 Solving 0.5625 + x = 0.970260919 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 = 0.970260919 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 0.970260919 + -0.5625 x = 0.970260919 + -0.5625 Combine like terms: 0.970260919 + -0.5625 = 0.407760919 x = 0.407760919 Simplifying x = 0.407760919Subproblem 2
x + 0.5625 = -0.970260919 Simplifying x + 0.5625 = -0.970260919 Reorder the terms: 0.5625 + x = -0.970260919 Solving 0.5625 + x = -0.970260919 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 = -0.970260919 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -0.970260919 + -0.5625 x = -0.970260919 + -0.5625 Combine like terms: -0.970260919 + -0.5625 = -1.532760919 x = -1.532760919 Simplifying x = -1.532760919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.407760919, -1.532760919}
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