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Simplifying 0.5x2 + 2x = 240 Reorder the terms: 2x + 0.5x2 = 240 Solving 2x + 0.5x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 2x + 0.5x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 2x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -480 + 4x + x2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 4x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 4x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 4x + x2 = 0 + 480 4x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 4x + x2 = 480 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 480 + 4 Reorder the terms: 4 + 4x + x2 = 480 + 4 Combine like terms: 480 + 4 = 484 4 + 4x + x2 = 484 Factor a perfect square on the left side: (x + 2)(x + 2) = 484 Calculate the square root of the right side: 22 Break this problem into two subproblems by setting (x + 2) equal to 22 and -22.Subproblem 1
x + 2 = 22 Simplifying x + 2 = 22 Reorder the terms: 2 + x = 22 Solving 2 + x = 22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 22 + -2 Combine like terms: 2 + -2 = 0 0 + x = 22 + -2 x = 22 + -2 Combine like terms: 22 + -2 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 2 = -22 Simplifying x + 2 = -22 Reorder the terms: 2 + x = -22 Solving 2 + x = -22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -22 + -2 Combine like terms: 2 + -2 = 0 0 + x = -22 + -2 x = -22 + -2 Combine like terms: -22 + -2 = -24 x = -24 Simplifying x = -24Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -24}
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