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Simplifying (0.64 + -3.2x + 4x2) * 0.016 = 0 Reorder the terms for easier multiplication: 0.016(0.64 + -3.2x + 4x2) = 0 (0.64 * 0.016 + -3.2x * 0.016 + 4x2 * 0.016) = 0 (0.01024 + -0.0512x + 0.064x2) = 0 Solving 0.01024 + -0.0512x + 0.064x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.064 the coefficient of the squared term: Divide each side by '0.064'. 0.16 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -0.8x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -0.8x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -0.8x + x2 = 0 + -0.16 -0.8x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -0.8x + x2 = -0.16 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.16 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.16 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.16 + -0.8x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.4) equal to 0.00 and 0.00.Subproblem 1
x + -0.4 = 0.00 Simplifying x + -0.4 = 0.00 Reorder the terms: -0.4 + x = 0.00 Solving -0.4 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.00 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.00 + 0.4 x = 0.00 + 0.4 Combine like terms: 0.00 + 0.4 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.4 = 0.00 Simplifying x + -0.4 = 0.00 Reorder the terms: -0.4 + x = 0.00 Solving -0.4 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.00 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.00 + 0.4 x = 0.00 + 0.4 Combine like terms: 0.00 + 0.4 = 0.4 x = 0.4 Simplifying x = 0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, 0.4}
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