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Simplifying 0.3x2 + 3x + -180 = 0 Reorder the terms: -180 + 3x + 0.3x2 = 0 Solving -180 + 3x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -600 + 10x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + 10x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 10x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 10x + x2 = 0 + 600 10x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 10x + x2 = 600 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 = 600 + 25 Reorder the terms: 25 + 10x + x2 = 600 + 25 Combine like terms: 600 + 25 = 625 25 + 10x + x2 = 625 Factor a perfect square on the left side: (x + 5)(x + 5) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + 5) equal to 25 and -25.Subproblem 1
x + 5 = 25 Simplifying x + 5 = 25 Reorder the terms: 5 + x = 25 Solving 5 + x = 25 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 = 25 + -5 Combine like terms: 5 + -5 = 0 0 + x = 25 + -5 x = 25 + -5 Combine like terms: 25 + -5 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 5 = -25 Simplifying x + 5 = -25 Reorder the terms: 5 + x = -25 Solving 5 + x = -25 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 = -25 + -5 Combine like terms: 5 + -5 = 0 0 + x = -25 + -5 x = -25 + -5 Combine like terms: -25 + -5 = -30 x = -30 Simplifying x = -30Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -30}
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