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Simplifying 17x2 + 70x + -140 = 0 Reorder the terms: -140 + 70x + 17x2 = 0 Solving -140 + 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'. -8.235294118 + 4.117647059x + x2 = 0 Move the constant term to the right: Add '8.235294118' to each side of the equation. -8.235294118 + 4.117647059x + 8.235294118 + x2 = 0 + 8.235294118 Reorder the terms: -8.235294118 + 8.235294118 + 4.117647059x + x2 = 0 + 8.235294118 Combine like terms: -8.235294118 + 8.235294118 = 0.000000000 0.000000000 + 4.117647059x + x2 = 0 + 8.235294118 4.117647059x + x2 = 0 + 8.235294118 Combine like terms: 0 + 8.235294118 = 8.235294118 4.117647059x + x2 = 8.235294118 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 = 8.235294118 + 4.238754328 Reorder the terms: 4.238754328 + 4.117647059x + x2 = 8.235294118 + 4.238754328 Combine like terms: 8.235294118 + 4.238754328 = 12.474048446 4.238754328 + 4.117647059x + x2 = 12.474048446 Factor a perfect square on the left side: (x + 2.05882353)(x + 2.05882353) = 12.474048446 Calculate the square root of the right side: 3.531861895 Break this problem into two subproblems by setting (x + 2.05882353) equal to 3.531861895 and -3.531861895.Subproblem 1
x + 2.05882353 = 3.531861895 Simplifying x + 2.05882353 = 3.531861895 Reorder the terms: 2.05882353 + x = 3.531861895 Solving 2.05882353 + x = 3.531861895 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 = 3.531861895 + -2.05882353 Combine like terms: 2.05882353 + -2.05882353 = 0.00000000 0.00000000 + x = 3.531861895 + -2.05882353 x = 3.531861895 + -2.05882353 Combine like terms: 3.531861895 + -2.05882353 = 1.473038365 x = 1.473038365 Simplifying x = 1.473038365Subproblem 2
x + 2.05882353 = -3.531861895 Simplifying x + 2.05882353 = -3.531861895 Reorder the terms: 2.05882353 + x = -3.531861895 Solving 2.05882353 + x = -3.531861895 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 = -3.531861895 + -2.05882353 Combine like terms: 2.05882353 + -2.05882353 = 0.00000000 0.00000000 + x = -3.531861895 + -2.05882353 x = -3.531861895 + -2.05882353 Combine like terms: -3.531861895 + -2.05882353 = -5.590685425 x = -5.590685425 Simplifying x = -5.590685425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.473038365, -5.590685425}
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