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Simplifying 3x2 + 17x = 89 Reorder the terms: 17x + 3x2 = 89 Solving 17x + 3x2 = 89 Solving for variable 'x'. Reorder the terms: -89 + 17x + 3x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -89 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -29.66666667 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '29.66666667' to each side of the equation. -29.66666667 + 5.666666667x + 29.66666667 + x2 = 0 + 29.66666667 Reorder the terms: -29.66666667 + 29.66666667 + 5.666666667x + x2 = 0 + 29.66666667 Combine like terms: -29.66666667 + 29.66666667 = 0.00000000 0.00000000 + 5.666666667x + x2 = 0 + 29.66666667 5.666666667x + x2 = 0 + 29.66666667 Combine like terms: 0 + 29.66666667 = 29.66666667 5.666666667x + x2 = 29.66666667 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = 29.66666667 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 29.66666667 + 8.027777782 Combine like terms: 29.66666667 + 8.027777782 = 37.694444452 8.027777782 + 5.666666667x + x2 = 37.694444452 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 37.694444452 Calculate the square root of the right side: 6.139580153 Break this problem into two subproblems by setting (x + 2.833333334) equal to 6.139580153 and -6.139580153.Subproblem 1
x + 2.833333334 = 6.139580153 Simplifying x + 2.833333334 = 6.139580153 Reorder the terms: 2.833333334 + x = 6.139580153 Solving 2.833333334 + x = 6.139580153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 6.139580153 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 6.139580153 + -2.833333334 x = 6.139580153 + -2.833333334 Combine like terms: 6.139580153 + -2.833333334 = 3.306246819 x = 3.306246819 Simplifying x = 3.306246819Subproblem 2
x + 2.833333334 = -6.139580153 Simplifying x + 2.833333334 = -6.139580153 Reorder the terms: 2.833333334 + x = -6.139580153 Solving 2.833333334 + x = -6.139580153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -6.139580153 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -6.139580153 + -2.833333334 x = -6.139580153 + -2.833333334 Combine like terms: -6.139580153 + -2.833333334 = -8.972913487 x = -8.972913487 Simplifying x = -8.972913487Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.306246819, -8.972913487}
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