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Simplifying 8 = -0.01x2 + -0.1x + 38 Reorder the terms: 8 = 38 + -0.1x + -0.01x2 Solving 8 = 38 + -0.1x + -0.01x2 Solving for variable 'x'. Combine like terms: 8 + -38 = -30 -30 + 0.1x + 0.01x2 = 38 + -0.1x + -0.01x2 + -38 + 0.1x + 0.01x2 Reorder the terms: -30 + 0.1x + 0.01x2 = 38 + -38 + -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: 38 + -38 = 0 -30 + 0.1x + 0.01x2 = 0 + -0.1x + 0.1x + -0.01x2 + 0.01x2 -30 + 0.1x + 0.01x2 = -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: -0.1x + 0.1x = 0.0 -30 + 0.1x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -30 + 0.1x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -30 + 0.1x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -3000 + 10x + x2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 10x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 10x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 10x + x2 = 0 + 3000 10x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 10x + x2 = 3000 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3000 + 25 Reorder the terms: 25 + 10x + x2 = 3000 + 25 Combine like terms: 3000 + 25 = 3025 25 + 10x + x2 = 3025 Factor a perfect square on the left side: (x + 5)(x + 5) = 3025 Calculate the square root of the right side: 55 Break this problem into two subproblems by setting (x + 5) equal to 55 and -55.Subproblem 1
x + 5 = 55 Simplifying x + 5 = 55 Reorder the terms: 5 + x = 55 Solving 5 + x = 55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 55 + -5 Combine like terms: 5 + -5 = 0 0 + x = 55 + -5 x = 55 + -5 Combine like terms: 55 + -5 = 50 x = 50 Simplifying x = 50Subproblem 2
x + 5 = -55 Simplifying x + 5 = -55 Reorder the terms: 5 + x = -55 Solving 5 + x = -55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -55 + -5 Combine like terms: 5 + -5 = 0 0 + x = -55 + -5 x = -55 + -5 Combine like terms: -55 + -5 = -60 x = -60 Simplifying x = -60Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -60}
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