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Simplifying -16x2 + 16x + 0 = 3.96 Reorder the terms: 0 + 16x + -16x2 = 3.96 Remove the zero: 16x + -16x2 = 3.96 Solving 16x + -16x2 = 3.96 Solving for variable 'x'. Reorder the terms: -3.96 + 16x + -16x2 = 3.96 + -3.96 Combine like terms: 3.96 + -3.96 = 0.00 -3.96 + 16x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.2475 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.2475' to each side of the equation. 0.2475 + -1x + -0.2475 + x2 = 0.00 + -0.2475 Reorder the terms: 0.2475 + -0.2475 + -1x + x2 = 0.00 + -0.2475 Combine like terms: 0.2475 + -0.2475 = 0.0000 0.0000 + -1x + x2 = 0.00 + -0.2475 -1x + x2 = 0.00 + -0.2475 Combine like terms: 0.00 + -0.2475 = -0.2475 -1x + x2 = -0.2475 The x term is -1x. 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. -1x + 0.25 + x2 = -0.2475 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.2475 + 0.25 Combine like terms: -0.2475 + 0.25 = 0.0025 0.25 + -1x + x2 = 0.0025 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -0.5) equal to 0.05 and -0.05.Subproblem 1
x + -0.5 = 0.05 Simplifying x + -0.5 = 0.05 Reorder the terms: -0.5 + x = 0.05 Solving -0.5 + x = 0.05 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 = 0.05 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.05 + 0.5 x = 0.05 + 0.5 Combine like terms: 0.05 + 0.5 = 0.55 x = 0.55 Simplifying x = 0.55Subproblem 2
x + -0.5 = -0.05 Simplifying x + -0.5 = -0.05 Reorder the terms: -0.5 + x = -0.05 Solving -0.5 + x = -0.05 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 = -0.05 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.05 + 0.5 x = -0.05 + 0.5 Combine like terms: -0.05 + 0.5 = 0.45 x = 0.45 Simplifying x = 0.45Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.55, 0.45}
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