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Simplifying 17x2 + 70x + -105 = 0 Reorder the terms: -105 + 70x + 17x2 = 0 Solving -105 + 70x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -6.176470588 + 4.117647059x + x2 = 0 Move the constant term to the right: Add '6.176470588' to each side of the equation. -6.176470588 + 4.117647059x + 6.176470588 + x2 = 0 + 6.176470588 Reorder the terms: -6.176470588 + 6.176470588 + 4.117647059x + x2 = 0 + 6.176470588 Combine like terms: -6.176470588 + 6.176470588 = 0.000000000 0.000000000 + 4.117647059x + x2 = 0 + 6.176470588 4.117647059x + x2 = 0 + 6.176470588 Combine like terms: 0 + 6.176470588 = 6.176470588 4.117647059x + x2 = 6.176470588 The x term is 4.117647059x. Take half its coefficient (2.05882353). Square it (4.238754328) and add it to both sides. Add '4.238754328' to each side of the equation. 4.117647059x + 4.238754328 + x2 = 6.176470588 + 4.238754328 Reorder the terms: 4.238754328 + 4.117647059x + x2 = 6.176470588 + 4.238754328 Combine like terms: 6.176470588 + 4.238754328 = 10.415224916 4.238754328 + 4.117647059x + x2 = 10.415224916 Factor a perfect square on the left side: (x + 2.05882353)(x + 2.05882353) = 10.415224916 Calculate the square root of the right side: 3.227262759 Break this problem into two subproblems by setting (x + 2.05882353) equal to 3.227262759 and -3.227262759.Subproblem 1
x + 2.05882353 = 3.227262759 Simplifying x + 2.05882353 = 3.227262759 Reorder the terms: 2.05882353 + x = 3.227262759 Solving 2.05882353 + x = 3.227262759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.05882353' to each side of the equation. 2.05882353 + -2.05882353 + x = 3.227262759 + -2.05882353 Combine like terms: 2.05882353 + -2.05882353 = 0.00000000 0.00000000 + x = 3.227262759 + -2.05882353 x = 3.227262759 + -2.05882353 Combine like terms: 3.227262759 + -2.05882353 = 1.168439229 x = 1.168439229 Simplifying x = 1.168439229Subproblem 2
x + 2.05882353 = -3.227262759 Simplifying x + 2.05882353 = -3.227262759 Reorder the terms: 2.05882353 + x = -3.227262759 Solving 2.05882353 + x = -3.227262759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.05882353' to each side of the equation. 2.05882353 + -2.05882353 + x = -3.227262759 + -2.05882353 Combine like terms: 2.05882353 + -2.05882353 = 0.00000000 0.00000000 + x = -3.227262759 + -2.05882353 x = -3.227262759 + -2.05882353 Combine like terms: -3.227262759 + -2.05882353 = -5.286086289 x = -5.286086289 Simplifying x = -5.286086289Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.168439229, -5.286086289}
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