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Simplifying 96 = 0.5(x + 4) * x Reorder the terms: 96 = 0.5(4 + x) * x Reorder the terms for easier multiplication: 96 = 0.5x(4 + x) 96 = (4 * 0.5x + x * 0.5x) 96 = (2x + 0.5x2) Solving 96 = 2x + 0.5x2 Solving for variable 'x'. Reorder the terms: 96 + -2x + -0.5x2 = 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: 2x + -2x = 0 96 + -2x + -0.5x2 = 0 + 0.5x2 + -0.5x2 96 + -2x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 96 + -2x + -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'. -192 + 4x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 4x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 4x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 4x + x2 = 0 + 192 4x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 4x + x2 = 192 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 = 192 + 4 Reorder the terms: 4 + 4x + x2 = 192 + 4 Combine like terms: 192 + 4 = 196 4 + 4x + x2 = 196 Factor a perfect square on the left side: (x + 2)(x + 2) = 196 Calculate the square root of the right side: 14 Break this problem into two subproblems by setting (x + 2) equal to 14 and -14.Subproblem 1
x + 2 = 14 Simplifying x + 2 = 14 Reorder the terms: 2 + x = 14 Solving 2 + x = 14 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 = 14 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14 + -2 x = 14 + -2 Combine like terms: 14 + -2 = 12 x = 12 Simplifying x = 12Subproblem 2
x + 2 = -14 Simplifying x + 2 = -14 Reorder the terms: 2 + x = -14 Solving 2 + x = -14 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 = -14 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14 + -2 x = -14 + -2 Combine like terms: -14 + -2 = -16 x = -16 Simplifying x = -16Solution
The solution to the problem is based on the solutions from the subproblems. x = {12, -16}
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