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Simplifying 4x + 0.5x2 = 120 Solving 4x + 0.5x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 4x + 0.5x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 4x + 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'. -240 + 8x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 8x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 8x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 8x + x2 = 0 + 240 8x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 8x + x2 = 240 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 = 240 + 16 Reorder the terms: 16 + 8x + x2 = 240 + 16 Combine like terms: 240 + 16 = 256 16 + 8x + x2 = 256 Factor a perfect square on the left side: (x + 4)(x + 4) = 256 Calculate the square root of the right side: 16 Break this problem into two subproblems by setting (x + 4) equal to 16 and -16.Subproblem 1
x + 4 = 16 Simplifying x + 4 = 16 Reorder the terms: 4 + x = 16 Solving 4 + x = 16 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 = 16 + -4 Combine like terms: 4 + -4 = 0 0 + x = 16 + -4 x = 16 + -4 Combine like terms: 16 + -4 = 12 x = 12 Simplifying x = 12Subproblem 2
x + 4 = -16 Simplifying x + 4 = -16 Reorder the terms: 4 + x = -16 Solving 4 + x = -16 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 = -16 + -4 Combine like terms: 4 + -4 = 0 0 + x = -16 + -4 x = -16 + -4 Combine like terms: -16 + -4 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -20}
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