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Simplifying -0.01x2 + -0.3x + 10 = 0 Reorder the terms: 10 + -0.3x + -0.01x2 = 0 Solving 10 + -0.3x + -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'. -1000 + 30x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 30x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 30x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 30x + x2 = 0 + 1000 30x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 30x + x2 = 1000 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 1000 + 225 Reorder the terms: 225 + 30x + x2 = 1000 + 225 Combine like terms: 1000 + 225 = 1225 225 + 30x + x2 = 1225 Factor a perfect square on the left side: (x + 15)(x + 15) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (x + 15) equal to 35 and -35.Subproblem 1
x + 15 = 35 Simplifying x + 15 = 35 Reorder the terms: 15 + x = 35 Solving 15 + x = 35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 35 + -15 Combine like terms: 15 + -15 = 0 0 + x = 35 + -15 x = 35 + -15 Combine like terms: 35 + -15 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 15 = -35 Simplifying x + 15 = -35 Reorder the terms: 15 + x = -35 Solving 15 + x = -35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -35 + -15 Combine like terms: 15 + -15 = 0 0 + x = -35 + -15 x = -35 + -15 Combine like terms: -35 + -15 = -50 x = -50 Simplifying x = -50Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -50}
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