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Simplifying 0 = 0.5x2 + 4x + -280 Reorder the terms: 0 = -280 + 4x + 0.5x2 Solving 0 = -280 + 4x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + 280 = 280 280 + -4x + -0.5x2 = -280 + 4x + 0.5x2 + 280 + -4x + -0.5x2 Reorder the terms: 280 + -4x + -0.5x2 = -280 + 280 + 4x + -4x + 0.5x2 + -0.5x2 Combine like terms: -280 + 280 = 0 280 + -4x + -0.5x2 = 0 + 4x + -4x + 0.5x2 + -0.5x2 280 + -4x + -0.5x2 = 4x + -4x + 0.5x2 + -0.5x2 Combine like terms: 4x + -4x = 0 280 + -4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 280 + -4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 280 + -4x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -560 + 8x + x2 = 0 Move the constant term to the right: Add '560' to each side of the equation. -560 + 8x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + 8x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + 8x + x2 = 0 + 560 8x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 8x + x2 = 560 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 560 + 16 Reorder the terms: 16 + 8x + x2 = 560 + 16 Combine like terms: 560 + 16 = 576 16 + 8x + x2 = 576 Factor a perfect square on the left side: (x + 4)(x + 4) = 576 Calculate the square root of the right side: 24 Break this problem into two subproblems by setting (x + 4) equal to 24 and -24.Subproblem 1
x + 4 = 24 Simplifying x + 4 = 24 Reorder the terms: 4 + x = 24 Solving 4 + x = 24 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 24 + -4 Combine like terms: 4 + -4 = 0 0 + x = 24 + -4 x = 24 + -4 Combine like terms: 24 + -4 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 4 = -24 Simplifying x + 4 = -24 Reorder the terms: 4 + x = -24 Solving 4 + x = -24 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -24 + -4 Combine like terms: 4 + -4 = 0 0 + x = -24 + -4 x = -24 + -4 Combine like terms: -24 + -4 = -28 x = -28 Simplifying x = -28Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -28}
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