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Simplifying 0.5x2 + 2x + -48 = 0 Reorder the terms: -48 + 2x + 0.5x2 = 0 Solving -48 + 2x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -96 + 4x + x2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 4x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 4x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 4x + x2 = 0 + 96 4x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 4x + x2 = 96 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 = 96 + 4 Reorder the terms: 4 + 4x + x2 = 96 + 4 Combine like terms: 96 + 4 = 100 4 + 4x + x2 = 100 Factor a perfect square on the left side: (x + 2)(x + 2) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + 2) equal to 10 and -10.Subproblem 1
x + 2 = 10 Simplifying x + 2 = 10 Reorder the terms: 2 + x = 10 Solving 2 + x = 10 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 = 10 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10 + -2 x = 10 + -2 Combine like terms: 10 + -2 = 8 x = 8 Simplifying x = 8Subproblem 2
x + 2 = -10 Simplifying x + 2 = -10 Reorder the terms: 2 + x = -10 Solving 2 + x = -10 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 = -10 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10 + -2 x = -10 + -2 Combine like terms: -10 + -2 = -12 x = -12 Simplifying x = -12Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -12}
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