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Simplifying 32 + 5x + -4.9x2 = 0 Solving 32 + 5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -6.530612245 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '6.530612245' to each side of the equation. -6.530612245 + -1.020408163x + 6.530612245 + x2 = 0 + 6.530612245 Reorder the terms: -6.530612245 + 6.530612245 + -1.020408163x + x2 = 0 + 6.530612245 Combine like terms: -6.530612245 + 6.530612245 = 0.000000000 0.000000000 + -1.020408163x + x2 = 0 + 6.530612245 -1.020408163x + x2 = 0 + 6.530612245 Combine like terms: 0 + 6.530612245 = 6.530612245 -1.020408163x + x2 = 6.530612245 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 6.530612245 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 6.530612245 + 0.2603082048 Combine like terms: 6.530612245 + 0.2603082048 = 6.7909204498 0.2603082048 + -1.020408163x + x2 = 6.7909204498 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 6.7909204498 Calculate the square root of the right side: 2.605939456 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 2.605939456 and -2.605939456.Subproblem 1
x + -0.5102040815 = 2.605939456 Simplifying x + -0.5102040815 = 2.605939456 Reorder the terms: -0.5102040815 + x = 2.605939456 Solving -0.5102040815 + x = 2.605939456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 2.605939456 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 2.605939456 + 0.5102040815 x = 2.605939456 + 0.5102040815 Combine like terms: 2.605939456 + 0.5102040815 = 3.1161435375 x = 3.1161435375 Simplifying x = 3.1161435375Subproblem 2
x + -0.5102040815 = -2.605939456 Simplifying x + -0.5102040815 = -2.605939456 Reorder the terms: -0.5102040815 + x = -2.605939456 Solving -0.5102040815 + x = -2.605939456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -2.605939456 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -2.605939456 + 0.5102040815 x = -2.605939456 + 0.5102040815 Combine like terms: -2.605939456 + 0.5102040815 = -2.0957353745 x = -2.0957353745 Simplifying x = -2.0957353745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1161435375, -2.0957353745}
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