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Simplifying 29x2 + 10x + -21 = 0 Reorder the terms: -21 + 10x + 29x2 = 0 Solving -21 + 10x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.724137931 + 0.3448275862x + x2 = 0 Move the constant term to the right: Add '0.724137931' to each side of the equation. -0.724137931 + 0.3448275862x + 0.724137931 + x2 = 0 + 0.724137931 Reorder the terms: -0.724137931 + 0.724137931 + 0.3448275862x + x2 = 0 + 0.724137931 Combine like terms: -0.724137931 + 0.724137931 = 0.000000000 0.000000000 + 0.3448275862x + x2 = 0 + 0.724137931 0.3448275862x + x2 = 0 + 0.724137931 Combine like terms: 0 + 0.724137931 = 0.724137931 0.3448275862x + x2 = 0.724137931 The x term is 0.3448275862x. Take half its coefficient (0.1724137931). Square it (0.02972651605) and add it to both sides. Add '0.02972651605' to each side of the equation. 0.3448275862x + 0.02972651605 + x2 = 0.724137931 + 0.02972651605 Reorder the terms: 0.02972651605 + 0.3448275862x + x2 = 0.724137931 + 0.02972651605 Combine like terms: 0.724137931 + 0.02972651605 = 0.75386444705 0.02972651605 + 0.3448275862x + x2 = 0.75386444705 Factor a perfect square on the left side: (x + 0.1724137931)(x + 0.1724137931) = 0.75386444705 Calculate the square root of the right side: 0.868253677 Break this problem into two subproblems by setting (x + 0.1724137931) equal to 0.868253677 and -0.868253677.Subproblem 1
x + 0.1724137931 = 0.868253677 Simplifying x + 0.1724137931 = 0.868253677 Reorder the terms: 0.1724137931 + x = 0.868253677 Solving 0.1724137931 + x = 0.868253677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1724137931' to each side of the equation. 0.1724137931 + -0.1724137931 + x = 0.868253677 + -0.1724137931 Combine like terms: 0.1724137931 + -0.1724137931 = 0.0000000000 0.0000000000 + x = 0.868253677 + -0.1724137931 x = 0.868253677 + -0.1724137931 Combine like terms: 0.868253677 + -0.1724137931 = 0.6958398839 x = 0.6958398839 Simplifying x = 0.6958398839Subproblem 2
x + 0.1724137931 = -0.868253677 Simplifying x + 0.1724137931 = -0.868253677 Reorder the terms: 0.1724137931 + x = -0.868253677 Solving 0.1724137931 + x = -0.868253677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1724137931' to each side of the equation. 0.1724137931 + -0.1724137931 + x = -0.868253677 + -0.1724137931 Combine like terms: 0.1724137931 + -0.1724137931 = 0.0000000000 0.0000000000 + x = -0.868253677 + -0.1724137931 x = -0.868253677 + -0.1724137931 Combine like terms: -0.868253677 + -0.1724137931 = -1.0406674701 x = -1.0406674701 Simplifying x = -1.0406674701Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6958398839, -1.0406674701}
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