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Simplifying 286 = x(0.5x + 2) Reorder the terms: 286 = x(2 + 0.5x) 286 = (2 * x + 0.5x * x) 286 = (2x + 0.5x2) Solving 286 = 2x + 0.5x2 Solving for variable 'x'. Reorder the terms: 286 + -2x + -0.5x2 = 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: 2x + -2x = 0 286 + -2x + -0.5x2 = 0 + 0.5x2 + -0.5x2 286 + -2x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 286 + -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'. -572 + 4x + x2 = 0 Move the constant term to the right: Add '572' to each side of the equation. -572 + 4x + 572 + x2 = 0 + 572 Reorder the terms: -572 + 572 + 4x + x2 = 0 + 572 Combine like terms: -572 + 572 = 0 0 + 4x + x2 = 0 + 572 4x + x2 = 0 + 572 Combine like terms: 0 + 572 = 572 4x + x2 = 572 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 = 572 + 4 Reorder the terms: 4 + 4x + x2 = 572 + 4 Combine like terms: 572 + 4 = 576 4 + 4x + x2 = 576 Factor a perfect square on the left side: (x + 2)(x + 2) = 576 Calculate the square root of the right side: 24 Break this problem into two subproblems by setting (x + 2) equal to 24 and -24.Subproblem 1
x + 2 = 24 Simplifying x + 2 = 24 Reorder the terms: 2 + x = 24 Solving 2 + x = 24 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 = 24 + -2 Combine like terms: 2 + -2 = 0 0 + x = 24 + -2 x = 24 + -2 Combine like terms: 24 + -2 = 22 x = 22 Simplifying x = 22Subproblem 2
x + 2 = -24 Simplifying x + 2 = -24 Reorder the terms: 2 + x = -24 Solving 2 + x = -24 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 = -24 + -2 Combine like terms: 2 + -2 = 0 0 + x = -24 + -2 x = -24 + -2 Combine like terms: -24 + -2 = -26 x = -26 Simplifying x = -26Solution
The solution to the problem is based on the solutions from the subproblems. x = {22, -26}
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