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Simplifying 0.4x2 + 9 = 15x Reorder the terms: 9 + 0.4x2 = 15x Solving 9 + 0.4x2 = 15x Solving for variable 'x'. Reorder the terms: 9 + -15x + 0.4x2 = 15x + -15x Combine like terms: 15x + -15x = 0 9 + -15x + 0.4x2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 22.5 + -37.5x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -37.5x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -37.5x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -37.5x + x2 = 0 + -22.5 -37.5x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -37.5x + x2 = -22.5 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = -22.5 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = -22.5 + 351.5625 Combine like terms: -22.5 + 351.5625 = 329.0625 351.5625 + -37.5x + x2 = 329.0625 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 329.0625 Calculate the square root of the right side: 18.140079934 Break this problem into two subproblems by setting (x + -18.75) equal to 18.140079934 and -18.140079934.Subproblem 1
x + -18.75 = 18.140079934 Simplifying x + -18.75 = 18.140079934 Reorder the terms: -18.75 + x = 18.140079934 Solving -18.75 + x = 18.140079934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 18.140079934 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 18.140079934 + 18.75 x = 18.140079934 + 18.75 Combine like terms: 18.140079934 + 18.75 = 36.890079934 x = 36.890079934 Simplifying x = 36.890079934Subproblem 2
x + -18.75 = -18.140079934 Simplifying x + -18.75 = -18.140079934 Reorder the terms: -18.75 + x = -18.140079934 Solving -18.75 + x = -18.140079934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = -18.140079934 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -18.140079934 + 18.75 x = -18.140079934 + 18.75 Combine like terms: -18.140079934 + 18.75 = 0.609920066 x = 0.609920066 Simplifying x = 0.609920066Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.890079934, 0.609920066}
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