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