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Simplifying 0.4x(x + 200) = 900 Reorder the terms: 0.4x(200 + x) = 900 (200 * 0.4x + x * 0.4x) = 900 (80x + 0.4x2) = 900 Solving 80x + 0.4x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 80x + 0.4x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 80x + 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'. -2250 + 200x + x2 = 0 Move the constant term to the right: Add '2250' to each side of the equation. -2250 + 200x + 2250 + x2 = 0 + 2250 Reorder the terms: -2250 + 2250 + 200x + x2 = 0 + 2250 Combine like terms: -2250 + 2250 = 0 0 + 200x + x2 = 0 + 2250 200x + x2 = 0 + 2250 Combine like terms: 0 + 2250 = 2250 200x + x2 = 2250 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 2250 + 10000 Reorder the terms: 10000 + 200x + x2 = 2250 + 10000 Combine like terms: 2250 + 10000 = 12250 10000 + 200x + x2 = 12250 Factor a perfect square on the left side: (x + 100)(x + 100) = 12250 Calculate the square root of the right side: 110.679718106 Break this problem into two subproblems by setting (x + 100) equal to 110.679718106 and -110.679718106.Subproblem 1
x + 100 = 110.679718106 Simplifying x + 100 = 110.679718106 Reorder the terms: 100 + x = 110.679718106 Solving 100 + x = 110.679718106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 110.679718106 + -100 Combine like terms: 100 + -100 = 0 0 + x = 110.679718106 + -100 x = 110.679718106 + -100 Combine like terms: 110.679718106 + -100 = 10.679718106 x = 10.679718106 Simplifying x = 10.679718106Subproblem 2
x + 100 = -110.679718106 Simplifying x + 100 = -110.679718106 Reorder the terms: 100 + x = -110.679718106 Solving 100 + x = -110.679718106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -110.679718106 + -100 Combine like terms: 100 + -100 = 0 0 + x = -110.679718106 + -100 x = -110.679718106 + -100 Combine like terms: -110.679718106 + -100 = -210.679718106 x = -210.679718106 Simplifying x = -210.679718106Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.679718106, -210.679718106}
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