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Simplifying 4x2 + 2x + -41.999 = 0 Reorder the terms: -41.999 + 2x + 4x2 = 0 Solving -41.999 + 2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.49975 + 0.5x + x2 = 0 Move the constant term to the right: Add '10.49975' to each side of the equation. -10.49975 + 0.5x + 10.49975 + x2 = 0 + 10.49975 Reorder the terms: -10.49975 + 10.49975 + 0.5x + x2 = 0 + 10.49975 Combine like terms: -10.49975 + 10.49975 = 0.00000 0.00000 + 0.5x + x2 = 0 + 10.49975 0.5x + x2 = 0 + 10.49975 Combine like terms: 0 + 10.49975 = 10.49975 0.5x + x2 = 10.49975 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 10.49975 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 10.49975 + 0.0625 Combine like terms: 10.49975 + 0.0625 = 10.56225 0.0625 + 0.5x + x2 = 10.56225 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 10.56225 Calculate the square root of the right side: 3.249961538 Break this problem into two subproblems by setting (x + 0.25) equal to 3.249961538 and -3.249961538.Subproblem 1
x + 0.25 = 3.249961538 Simplifying x + 0.25 = 3.249961538 Reorder the terms: 0.25 + x = 3.249961538 Solving 0.25 + x = 3.249961538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.249961538 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.249961538 + -0.25 x = 3.249961538 + -0.25 Combine like terms: 3.249961538 + -0.25 = 2.999961538 x = 2.999961538 Simplifying x = 2.999961538Subproblem 2
x + 0.25 = -3.249961538 Simplifying x + 0.25 = -3.249961538 Reorder the terms: 0.25 + x = -3.249961538 Solving 0.25 + x = -3.249961538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.249961538 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.249961538 + -0.25 x = -3.249961538 + -0.25 Combine like terms: -3.249961538 + -0.25 = -3.499961538 x = -3.499961538 Simplifying x = -3.499961538Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.999961538, -3.499961538}
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