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Simplifying 3600 = 0.05x2 + 2.0x Reorder the terms: 3600 = 2.0x + 0.05x2 Solving 3600 = 2.0x + 0.05x2 Solving for variable 'x'. Reorder the terms: 3600 + -2.0x + -0.05x2 = 2.0x + -2.0x + 0.05x2 + -0.05x2 Combine like terms: 2.0x + -2.0x = 0.0 3600 + -2.0x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 3600 + -2.0x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 3600 + -2.0x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -72000 + 40x + x2 = 0 Move the constant term to the right: Add '72000' to each side of the equation. -72000 + 40x + 72000 + x2 = 0 + 72000 Reorder the terms: -72000 + 72000 + 40x + x2 = 0 + 72000 Combine like terms: -72000 + 72000 = 0 0 + 40x + x2 = 0 + 72000 40x + x2 = 0 + 72000 Combine like terms: 0 + 72000 = 72000 40x + x2 = 72000 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 72000 + 400 Reorder the terms: 400 + 40x + x2 = 72000 + 400 Combine like terms: 72000 + 400 = 72400 400 + 40x + x2 = 72400 Factor a perfect square on the left side: (x + 20)(x + 20) = 72400 Calculate the square root of the right side: 269.072480941 Break this problem into two subproblems by setting (x + 20) equal to 269.072480941 and -269.072480941.Subproblem 1
x + 20 = 269.072480941 Simplifying x + 20 = 269.072480941 Reorder the terms: 20 + x = 269.072480941 Solving 20 + x = 269.072480941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 269.072480941 + -20 Combine like terms: 20 + -20 = 0 0 + x = 269.072480941 + -20 x = 269.072480941 + -20 Combine like terms: 269.072480941 + -20 = 249.072480941 x = 249.072480941 Simplifying x = 249.072480941Subproblem 2
x + 20 = -269.072480941 Simplifying x + 20 = -269.072480941 Reorder the terms: 20 + x = -269.072480941 Solving 20 + x = -269.072480941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -269.072480941 + -20 Combine like terms: 20 + -20 = 0 0 + x = -269.072480941 + -20 x = -269.072480941 + -20 Combine like terms: -269.072480941 + -20 = -289.072480941 x = -289.072480941 Simplifying x = -289.072480941Solution
The solution to the problem is based on the solutions from the subproblems. x = {249.072480941, -289.072480941}
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