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Simplifying 0.5(x + 4) * x = 160 Reorder the terms: 0.5(4 + x) * x = 160 Reorder the terms for easier multiplication: 0.5x(4 + x) = 160 (4 * 0.5x + x * 0.5x) = 160 (2x + 0.5x2) = 160 Solving 2x + 0.5x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 2x + 0.5x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 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'. -320 + 4x + x2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + 4x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 4x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 4x + x2 = 0 + 320 4x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 4x + x2 = 320 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 = 320 + 4 Reorder the terms: 4 + 4x + x2 = 320 + 4 Combine like terms: 320 + 4 = 324 4 + 4x + x2 = 324 Factor a perfect square on the left side: (x + 2)(x + 2) = 324 Calculate the square root of the right side: 18 Break this problem into two subproblems by setting (x + 2) equal to 18 and -18.Subproblem 1
x + 2 = 18 Simplifying x + 2 = 18 Reorder the terms: 2 + x = 18 Solving 2 + x = 18 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 = 18 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18 + -2 x = 18 + -2 Combine like terms: 18 + -2 = 16 x = 16 Simplifying x = 16Subproblem 2
x + 2 = -18 Simplifying x + 2 = -18 Reorder the terms: 2 + x = -18 Solving 2 + x = -18 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 = -18 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18 + -2 x = -18 + -2 Combine like terms: -18 + -2 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, -20}
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