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Simplifying 0 = 0.4x2 + 10x + -240 Reorder the terms: 0 = -240 + 10x + 0.4x2 Solving 0 = -240 + 10x + 0.4x2 Solving for variable 'x'. Combine like terms: 0 + 240 = 240 240 + -10x + -0.4x2 = -240 + 10x + 0.4x2 + 240 + -10x + -0.4x2 Reorder the terms: 240 + -10x + -0.4x2 = -240 + 240 + 10x + -10x + 0.4x2 + -0.4x2 Combine like terms: -240 + 240 = 0 240 + -10x + -0.4x2 = 0 + 10x + -10x + 0.4x2 + -0.4x2 240 + -10x + -0.4x2 = 10x + -10x + 0.4x2 + -0.4x2 Combine like terms: 10x + -10x = 0 240 + -10x + -0.4x2 = 0 + 0.4x2 + -0.4x2 240 + -10x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 240 + -10x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -600 + 25x + x2 = 0 Move the constant term to the right: Add '600' to each side of the equation. -600 + 25x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + 25x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + 25x + x2 = 0 + 600 25x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 25x + x2 = 600 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 600 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 600 + 156.25 Combine like terms: 600 + 156.25 = 756.25 156.25 + 25x + x2 = 756.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 756.25 Calculate the square root of the right side: 27.5 Break this problem into two subproblems by setting (x + 12.5) equal to 27.5 and -27.5.Subproblem 1
x + 12.5 = 27.5 Simplifying x + 12.5 = 27.5 Reorder the terms: 12.5 + x = 27.5 Solving 12.5 + x = 27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 27.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 27.5 + -12.5 x = 27.5 + -12.5 Combine like terms: 27.5 + -12.5 = 15 x = 15 Simplifying x = 15Subproblem 2
x + 12.5 = -27.5 Simplifying x + 12.5 = -27.5 Reorder the terms: 12.5 + x = -27.5 Solving 12.5 + x = -27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -27.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -27.5 + -12.5 x = -27.5 + -12.5 Combine like terms: -27.5 + -12.5 = -40 x = -40 Simplifying x = -40Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -40}
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