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Simplifying 0.02x2 + 3x + -2000 = 0 Reorder the terms: -2000 + 3x + 0.02x2 = 0 Solving -2000 + 3x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. -100000 + 150x + x2 = 0 Move the constant term to the right: Add '100000' to each side of the equation. -100000 + 150x + 100000 + x2 = 0 + 100000 Reorder the terms: -100000 + 100000 + 150x + x2 = 0 + 100000 Combine like terms: -100000 + 100000 = 0 0 + 150x + x2 = 0 + 100000 150x + x2 = 0 + 100000 Combine like terms: 0 + 100000 = 100000 150x + x2 = 100000 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 = 100000 + 5625 Reorder the terms: 5625 + 150x + x2 = 100000 + 5625 Combine like terms: 100000 + 5625 = 105625 5625 + 150x + x2 = 105625 Factor a perfect square on the left side: (x + 75)(x + 75) = 105625 Calculate the square root of the right side: 325 Break this problem into two subproblems by setting (x + 75) equal to 325 and -325.Subproblem 1
x + 75 = 325 Simplifying x + 75 = 325 Reorder the terms: 75 + x = 325 Solving 75 + x = 325 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 = 325 + -75 Combine like terms: 75 + -75 = 0 0 + x = 325 + -75 x = 325 + -75 Combine like terms: 325 + -75 = 250 x = 250 Simplifying x = 250Subproblem 2
x + 75 = -325 Simplifying x + 75 = -325 Reorder the terms: 75 + x = -325 Solving 75 + x = -325 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 = -325 + -75 Combine like terms: 75 + -75 = 0 0 + x = -325 + -75 x = -325 + -75 Combine like terms: -325 + -75 = -400 x = -400 Simplifying x = -400Solution
The solution to the problem is based on the solutions from the subproblems. x = {250, -400}
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