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Simplifying 3.2x2 + -4.9x + 1.2 = 0 Reorder the terms: 1.2 + -4.9x + 3.2x2 = 0 Solving 1.2 + -4.9x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 0.375 + -1.53125x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -1.53125x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -1.53125x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -1.53125x + x2 = 0 + -0.375 -1.53125x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -1.53125x + x2 = -0.375 The x term is -1.53125x. Take half its coefficient (-0.765625). Square it (0.5861816406) and add it to both sides. Add '0.5861816406' to each side of the equation. -1.53125x + 0.5861816406 + x2 = -0.375 + 0.5861816406 Reorder the terms: 0.5861816406 + -1.53125x + x2 = -0.375 + 0.5861816406 Combine like terms: -0.375 + 0.5861816406 = 0.2111816406 0.5861816406 + -1.53125x + x2 = 0.2111816406 Factor a perfect square on the left side: (x + -0.765625)(x + -0.765625) = 0.2111816406 Calculate the square root of the right side: 0.459545037 Break this problem into two subproblems by setting (x + -0.765625) equal to 0.459545037 and -0.459545037.Subproblem 1
x + -0.765625 = 0.459545037 Simplifying x + -0.765625 = 0.459545037 Reorder the terms: -0.765625 + x = 0.459545037 Solving -0.765625 + x = 0.459545037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.765625' to each side of the equation. -0.765625 + 0.765625 + x = 0.459545037 + 0.765625 Combine like terms: -0.765625 + 0.765625 = 0.000000 0.000000 + x = 0.459545037 + 0.765625 x = 0.459545037 + 0.765625 Combine like terms: 0.459545037 + 0.765625 = 1.225170037 x = 1.225170037 Simplifying x = 1.225170037Subproblem 2
x + -0.765625 = -0.459545037 Simplifying x + -0.765625 = -0.459545037 Reorder the terms: -0.765625 + x = -0.459545037 Solving -0.765625 + x = -0.459545037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.765625' to each side of the equation. -0.765625 + 0.765625 + x = -0.459545037 + 0.765625 Combine like terms: -0.765625 + 0.765625 = 0.000000 0.000000 + x = -0.459545037 + 0.765625 x = -0.459545037 + 0.765625 Combine like terms: -0.459545037 + 0.765625 = 0.306079963 x = 0.306079963 Simplifying x = 0.306079963Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.225170037, 0.306079963}
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