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Simplifying 0.5x(x + 4) = 16 Reorder the terms: 0.5x(4 + x) = 16 (4 * 0.5x + x * 0.5x) = 16 (2x + 0.5x2) = 16 Solving 2x + 0.5x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 2x + 0.5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 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'. -32 + 4x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 4x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 4x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 4x + x2 = 0 + 32 4x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 4x + x2 = 32 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 = 32 + 4 Reorder the terms: 4 + 4x + x2 = 32 + 4 Combine like terms: 32 + 4 = 36 4 + 4x + x2 = 36 Factor a perfect square on the left side: (x + 2)(x + 2) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + 2) equal to 6 and -6.Subproblem 1
x + 2 = 6 Simplifying x + 2 = 6 Reorder the terms: 2 + x = 6 Solving 2 + x = 6 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 = 6 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6 + -2 x = 6 + -2 Combine like terms: 6 + -2 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 2 = -6 Simplifying x + 2 = -6 Reorder the terms: 2 + x = -6 Solving 2 + x = -6 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 = -6 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6 + -2 x = -6 + -2 Combine like terms: -6 + -2 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -8}
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