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Simplifying 17x2 + -138x + -290 = 0 Reorder the terms: -290 + -138x + 17x2 = 0 Solving -290 + -138x + 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'. -17.05882353 + -8.117647059x + x2 = 0 Move the constant term to the right: Add '17.05882353' to each side of the equation. -17.05882353 + -8.117647059x + 17.05882353 + x2 = 0 + 17.05882353 Reorder the terms: -17.05882353 + 17.05882353 + -8.117647059x + x2 = 0 + 17.05882353 Combine like terms: -17.05882353 + 17.05882353 = 0.00000000 0.00000000 + -8.117647059x + x2 = 0 + 17.05882353 -8.117647059x + x2 = 0 + 17.05882353 Combine like terms: 0 + 17.05882353 = 17.05882353 -8.117647059x + x2 = 17.05882353 The x term is -8.117647059x. Take half its coefficient (-4.05882353). Square it (16.47404845) and add it to both sides. Add '16.47404845' to each side of the equation. -8.117647059x + 16.47404845 + x2 = 17.05882353 + 16.47404845 Reorder the terms: 16.47404845 + -8.117647059x + x2 = 17.05882353 + 16.47404845 Combine like terms: 17.05882353 + 16.47404845 = 33.53287198 16.47404845 + -8.117647059x + x2 = 33.53287198 Factor a perfect square on the left side: (x + -4.05882353)(x + -4.05882353) = 33.53287198 Calculate the square root of the right side: 5.790757462 Break this problem into two subproblems by setting (x + -4.05882353) equal to 5.790757462 and -5.790757462.Subproblem 1
x + -4.05882353 = 5.790757462 Simplifying x + -4.05882353 = 5.790757462 Reorder the terms: -4.05882353 + x = 5.790757462 Solving -4.05882353 + x = 5.790757462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.05882353' to each side of the equation. -4.05882353 + 4.05882353 + x = 5.790757462 + 4.05882353 Combine like terms: -4.05882353 + 4.05882353 = 0.00000000 0.00000000 + x = 5.790757462 + 4.05882353 x = 5.790757462 + 4.05882353 Combine like terms: 5.790757462 + 4.05882353 = 9.849580992 x = 9.849580992 Simplifying x = 9.849580992Subproblem 2
x + -4.05882353 = -5.790757462 Simplifying x + -4.05882353 = -5.790757462 Reorder the terms: -4.05882353 + x = -5.790757462 Solving -4.05882353 + x = -5.790757462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.05882353' to each side of the equation. -4.05882353 + 4.05882353 + x = -5.790757462 + 4.05882353 Combine like terms: -4.05882353 + 4.05882353 = 0.00000000 0.00000000 + x = -5.790757462 + 4.05882353 x = -5.790757462 + 4.05882353 Combine like terms: -5.790757462 + 4.05882353 = -1.731933932 x = -1.731933932 Simplifying x = -1.731933932Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.849580992, -1.731933932}
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