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Simplifying 1.5x2 + 60x + -1800 = 0 Reorder the terms: -1800 + 60x + 1.5x2 = 0 Solving -1800 + 60x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -1200 + 40x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 40x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 40x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 40x + x2 = 0 + 1200 40x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 40x + x2 = 1200 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 1200 + 400 Reorder the terms: 400 + 40x + x2 = 1200 + 400 Combine like terms: 1200 + 400 = 1600 400 + 40x + x2 = 1600 Factor a perfect square on the left side: (x + 20)(x + 20) = 1600 Calculate the square root of the right side: 40 Break this problem into two subproblems by setting (x + 20) equal to 40 and -40.Subproblem 1
x + 20 = 40 Simplifying x + 20 = 40 Reorder the terms: 20 + x = 40 Solving 20 + x = 40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 40 + -20 Combine like terms: 20 + -20 = 0 0 + x = 40 + -20 x = 40 + -20 Combine like terms: 40 + -20 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 20 = -40 Simplifying x + 20 = -40 Reorder the terms: 20 + x = -40 Solving 20 + x = -40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -40 + -20 Combine like terms: 20 + -20 = 0 0 + x = -40 + -20 x = -40 + -20 Combine like terms: -40 + -20 = -60 x = -60 Simplifying x = -60Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -60}
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