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Simplifying 3x2 + 21x + -4x = 218 Reorder the terms: 21x + -4x + 3x2 = 218 Combine like terms: 21x + -4x = 17x 17x + 3x2 = 218 Solving 17x + 3x2 = 218 Solving for variable 'x'. Reorder the terms: -218 + 17x + 3x2 = 218 + -218 Combine like terms: 218 + -218 = 0 -218 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -72.66666667 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '72.66666667' to each side of the equation. -72.66666667 + 5.666666667x + 72.66666667 + x2 = 0 + 72.66666667 Reorder the terms: -72.66666667 + 72.66666667 + 5.666666667x + x2 = 0 + 72.66666667 Combine like terms: -72.66666667 + 72.66666667 = 0.00000000 0.00000000 + 5.666666667x + x2 = 0 + 72.66666667 5.666666667x + x2 = 0 + 72.66666667 Combine like terms: 0 + 72.66666667 = 72.66666667 5.666666667x + x2 = 72.66666667 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 = 72.66666667 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 72.66666667 + 8.027777782 Combine like terms: 72.66666667 + 8.027777782 = 80.694444452 8.027777782 + 5.666666667x + x2 = 80.694444452 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 80.694444452 Calculate the square root of the right side: 8.983008653 Break this problem into two subproblems by setting (x + 2.833333334) equal to 8.983008653 and -8.983008653.Subproblem 1
x + 2.833333334 = 8.983008653 Simplifying x + 2.833333334 = 8.983008653 Reorder the terms: 2.833333334 + x = 8.983008653 Solving 2.833333334 + x = 8.983008653 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 = 8.983008653 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 8.983008653 + -2.833333334 x = 8.983008653 + -2.833333334 Combine like terms: 8.983008653 + -2.833333334 = 6.149675319 x = 6.149675319 Simplifying x = 6.149675319Subproblem 2
x + 2.833333334 = -8.983008653 Simplifying x + 2.833333334 = -8.983008653 Reorder the terms: 2.833333334 + x = -8.983008653 Solving 2.833333334 + x = -8.983008653 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 = -8.983008653 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -8.983008653 + -2.833333334 x = -8.983008653 + -2.833333334 Combine like terms: -8.983008653 + -2.833333334 = -11.816341987 x = -11.816341987 Simplifying x = -11.816341987Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.149675319, -11.816341987}
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