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Simplifying 0.5x(x + -4) = 48 Reorder the terms: 0.5x(-4 + x) = 48 (-4 * 0.5x + x * 0.5x) = 48 (-2x + 0.5x2) = 48 Solving -2x + 0.5x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -2x + 0.5x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -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'. -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 = 12 x = 12 Simplifying x = 12Subproblem 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 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -8}
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