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Simplifying 8 = 9x + 18x2 Solving 8 = 9x + 18x2 Solving for variable 'x'. Reorder the terms: 8 + -9x + -18x2 = 9x + -9x + 18x2 + -18x2 Combine like terms: 9x + -9x = 0 8 + -9x + -18x2 = 0 + 18x2 + -18x2 8 + -9x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 8 + -9x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.4444444444 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.5x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.5x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.4444444444 0.5x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.5x + x2 = 0.4444444444 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.4444444444 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.4444444444 + 0.0625 Combine like terms: 0.4444444444 + 0.0625 = 0.5069444444 0.0625 + 0.5x + x2 = 0.5069444444 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.5069444444 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + 0.25) equal to 0.712000312 and -0.712000312.Subproblem 1
x + 0.25 = 0.712000312 Simplifying x + 0.25 = 0.712000312 Reorder the terms: 0.25 + x = 0.712000312 Solving 0.25 + x = 0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.712000312 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.712000312 + -0.25 x = 0.712000312 + -0.25 Combine like terms: 0.712000312 + -0.25 = 0.462000312 x = 0.462000312 Simplifying x = 0.462000312Subproblem 2
x + 0.25 = -0.712000312 Simplifying x + 0.25 = -0.712000312 Reorder the terms: 0.25 + x = -0.712000312 Solving 0.25 + x = -0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.712000312 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.712000312 + -0.25 x = -0.712000312 + -0.25 Combine like terms: -0.712000312 + -0.25 = -0.962000312 x = -0.962000312 Simplifying x = -0.962000312Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.462000312, -0.962000312}
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