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Simplifying 64 = 0.5(x2 + 8x) Reorder the terms: 64 = 0.5(8x + x2) 64 = (8x * 0.5 + x2 * 0.5) 64 = (4x + 0.5x2) Solving 64 = 4x + 0.5x2 Solving for variable 'x'. Reorder the terms: 64 + -4x + -0.5x2 = 4x + -4x + 0.5x2 + -0.5x2 Combine like terms: 4x + -4x = 0 64 + -4x + -0.5x2 = 0 + 0.5x2 + -0.5x2 64 + -4x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 64 + -4x + -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'. -128 + 8x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 8x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 8x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 8x + x2 = 0 + 128 8x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 8x + x2 = 128 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 128 + 16 Reorder the terms: 16 + 8x + x2 = 128 + 16 Combine like terms: 128 + 16 = 144 16 + 8x + x2 = 144 Factor a perfect square on the left side: (x + 4)(x + 4) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + 4) equal to 12 and -12.Subproblem 1
x + 4 = 12 Simplifying x + 4 = 12 Reorder the terms: 4 + x = 12 Solving 4 + x = 12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 12 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12 + -4 x = 12 + -4 Combine like terms: 12 + -4 = 8 x = 8 Simplifying x = 8Subproblem 2
x + 4 = -12 Simplifying x + 4 = -12 Reorder the terms: 4 + x = -12 Solving 4 + x = -12 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -12 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12 + -4 x = -12 + -4 Combine like terms: -12 + -4 = -16 x = -16 Simplifying x = -16Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -16}
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