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Simplifying 3x2 + 17x + -6.9 = 0 Reorder the terms: -6.9 + 17x + 3x2 = 0 Solving -6.9 + 17x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.3 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + 5.666666667x + 2.3 + x2 = 0 + 2.3 Reorder the terms: -2.3 + 2.3 + 5.666666667x + x2 = 0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + 5.666666667x + x2 = 0 + 2.3 5.666666667x + x2 = 0 + 2.3 Combine like terms: 0 + 2.3 = 2.3 5.666666667x + x2 = 2.3 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 = 2.3 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 2.3 + 8.027777782 Combine like terms: 2.3 + 8.027777782 = 10.327777782 8.027777782 + 5.666666667x + x2 = 10.327777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 10.327777782 Calculate the square root of the right side: 3.213686012 Break this problem into two subproblems by setting (x + 2.833333334) equal to 3.213686012 and -3.213686012.Subproblem 1
x + 2.833333334 = 3.213686012 Simplifying x + 2.833333334 = 3.213686012 Reorder the terms: 2.833333334 + x = 3.213686012 Solving 2.833333334 + x = 3.213686012 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 = 3.213686012 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 3.213686012 + -2.833333334 x = 3.213686012 + -2.833333334 Combine like terms: 3.213686012 + -2.833333334 = 0.380352678 x = 0.380352678 Simplifying x = 0.380352678Subproblem 2
x + 2.833333334 = -3.213686012 Simplifying x + 2.833333334 = -3.213686012 Reorder the terms: 2.833333334 + x = -3.213686012 Solving 2.833333334 + x = -3.213686012 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 = -3.213686012 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -3.213686012 + -2.833333334 x = -3.213686012 + -2.833333334 Combine like terms: -3.213686012 + -2.833333334 = -6.047019346 x = -6.047019346 Simplifying x = -6.047019346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.380352678, -6.047019346}
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