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Simplifying -0.01x2 + -2x + 300 = 0 Reorder the terms: 300 + -2x + -0.01x2 = 0 Solving 300 + -2x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -30000 + 200x + x2 = 0 Move the constant term to the right: Add '30000' to each side of the equation. -30000 + 200x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + 200x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + 200x + x2 = 0 + 30000 200x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 200x + x2 = 30000 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 = 30000 + 10000 Reorder the terms: 10000 + 200x + x2 = 30000 + 10000 Combine like terms: 30000 + 10000 = 40000 10000 + 200x + x2 = 40000 Factor a perfect square on the left side: (x + 100)(x + 100) = 40000 Calculate the square root of the right side: 200 Break this problem into two subproblems by setting (x + 100) equal to 200 and -200.Subproblem 1
x + 100 = 200 Simplifying x + 100 = 200 Reorder the terms: 100 + x = 200 Solving 100 + x = 200 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 = 200 + -100 Combine like terms: 100 + -100 = 0 0 + x = 200 + -100 x = 200 + -100 Combine like terms: 200 + -100 = 100 x = 100 Simplifying x = 100Subproblem 2
x + 100 = -200 Simplifying x + 100 = -200 Reorder the terms: 100 + x = -200 Solving 100 + x = -200 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 = -200 + -100 Combine like terms: 100 + -100 = 0 0 + x = -200 + -100 x = -200 + -100 Combine like terms: -200 + -100 = -300 x = -300 Simplifying x = -300Solution
The solution to the problem is based on the solutions from the subproblems. x = {100, -300}
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