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Simplifying -0.01x2 + -0.3x + 21 = 3 Reorder the terms: 21 + -0.3x + -0.01x2 = 3 Solving 21 + -0.3x + -0.01x2 = 3 Solving for variable 'x'. Reorder the terms: 21 + -3 + -0.3x + -0.01x2 = 3 + -3 Combine like terms: 21 + -3 = 18 18 + -0.3x + -0.01x2 = 3 + -3 Combine like terms: 3 + -3 = 0 18 + -0.3x + -0.01x2 = 0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -1800 + 30x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 30x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 30x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 30x + x2 = 0 + 1800 30x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 30x + x2 = 1800 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 = 1800 + 225 Reorder the terms: 225 + 30x + x2 = 1800 + 225 Combine like terms: 1800 + 225 = 2025 225 + 30x + x2 = 2025 Factor a perfect square on the left side: (x + 15)(x + 15) = 2025 Calculate the square root of the right side: 45 Break this problem into two subproblems by setting (x + 15) equal to 45 and -45.Subproblem 1
x + 15 = 45 Simplifying x + 15 = 45 Reorder the terms: 15 + x = 45 Solving 15 + x = 45 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 = 45 + -15 Combine like terms: 15 + -15 = 0 0 + x = 45 + -15 x = 45 + -15 Combine like terms: 45 + -15 = 30 x = 30 Simplifying x = 30Subproblem 2
x + 15 = -45 Simplifying x + 15 = -45 Reorder the terms: 15 + x = -45 Solving 15 + x = -45 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 = -45 + -15 Combine like terms: 15 + -15 = 0 0 + x = -45 + -15 x = -45 + -15 Combine like terms: -45 + -15 = -60 x = -60 Simplifying x = -60Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -60}
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