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Simplifying 2.5 = x(30 + 0.2x) 2.5 = (30 * x + 0.2x * x) 2.5 = (30x + 0.2x2) Solving 2.5 = 30x + 0.2x2 Solving for variable 'x'. Reorder the terms: 2.5 + -30x + -0.2x2 = 30x + -30x + 0.2x2 + -0.2x2 Combine like terms: 30x + -30x = 0 2.5 + -30x + -0.2x2 = 0 + 0.2x2 + -0.2x2 2.5 + -30x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 2.5 + -30x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -12.5 + 150x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 150x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 150x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 150x + x2 = 0 + 12.5 150x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 150x + x2 = 12.5 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 12.5 + 5625 Reorder the terms: 5625 + 150x + x2 = 12.5 + 5625 Combine like terms: 12.5 + 5625 = 5637.5 5625 + 150x + x2 = 5637.5 Factor a perfect square on the left side: (x + 75)(x + 75) = 5637.5 Calculate the square root of the right side: 75.083287088 Break this problem into two subproblems by setting (x + 75) equal to 75.083287088 and -75.083287088.Subproblem 1
x + 75 = 75.083287088 Simplifying x + 75 = 75.083287088 Reorder the terms: 75 + x = 75.083287088 Solving 75 + x = 75.083287088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 75.083287088 + -75 Combine like terms: 75 + -75 = 0 0 + x = 75.083287088 + -75 x = 75.083287088 + -75 Combine like terms: 75.083287088 + -75 = 0.083287088 x = 0.083287088 Simplifying x = 0.083287088Subproblem 2
x + 75 = -75.083287088 Simplifying x + 75 = -75.083287088 Reorder the terms: 75 + x = -75.083287088 Solving 75 + x = -75.083287088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -75.083287088 + -75 Combine like terms: 75 + -75 = 0 0 + x = -75.083287088 + -75 x = -75.083287088 + -75 Combine like terms: -75.083287088 + -75 = -150.083287088 x = -150.083287088 Simplifying x = -150.083287088Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.083287088, -150.083287088}
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