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Simplifying 0.5(32) * x2 + 16x = 2.56 Multiply 0.5 * 32 16x2 + 16x = 2.56 Reorder the terms: 16x + 16x2 = 2.56 Solving 16x + 16x2 = 2.56 Solving for variable 'x'. Reorder the terms: -2.56 + 16x + 16x2 = 2.56 + -2.56 Combine like terms: 2.56 + -2.56 = 0.00 -2.56 + 16x + 16x2 = 0.00 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.16 + x + x2 = 0.00 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + x + 0.16 + x2 = 0.00 + 0.16 Reorder the terms: -0.16 + 0.16 + x + x2 = 0.00 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + x + x2 = 0.00 + 0.16 x + x2 = 0.00 + 0.16 Combine like terms: 0.00 + 0.16 = 0.16 x + x2 = 0.16 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.16 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.16 + 0.25 Combine like terms: 0.16 + 0.25 = 0.41 1.25 + x2 = 0.41 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 0.5) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 0.5 = 0.640312424 Simplifying x + 0.5 = 0.640312424 Reorder the terms: 0.5 + x = 0.640312424 Solving 0.5 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.640312424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.640312424 + -0.5 x = 0.640312424 + -0.5 Combine like terms: 0.640312424 + -0.5 = 0.140312424 x = 0.140312424 Simplifying x = 0.140312424Subproblem 2
x + 0.5 = -0.640312424 Simplifying x + 0.5 = -0.640312424 Reorder the terms: 0.5 + x = -0.640312424 Solving 0.5 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.640312424 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.640312424 + -0.5 x = -0.640312424 + -0.5 Combine like terms: -0.640312424 + -0.5 = -1.140312424 x = -1.140312424 Simplifying x = -1.140312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140312424, -1.140312424}
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