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Simplifying 3x2 + 17x + 15 = 0 Reorder the terms: 15 + 17x + 3x2 = 0 Solving 15 + 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'. 5 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5.666666667x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5.666666667x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5.666666667x + x2 = 0 + -5 5.666666667x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5.666666667x + x2 = -5 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 = -5 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = -5 + 8.027777782 Combine like terms: -5 + 8.027777782 = 3.027777782 8.027777782 + 5.666666667x + x2 = 3.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 3.027777782 Calculate the square root of the right side: 1.740051086 Break this problem into two subproblems by setting (x + 2.833333334) equal to 1.740051086 and -1.740051086.Subproblem 1
x + 2.833333334 = 1.740051086 Simplifying x + 2.833333334 = 1.740051086 Reorder the terms: 2.833333334 + x = 1.740051086 Solving 2.833333334 + x = 1.740051086 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 = 1.740051086 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 1.740051086 + -2.833333334 x = 1.740051086 + -2.833333334 Combine like terms: 1.740051086 + -2.833333334 = -1.093282248 x = -1.093282248 Simplifying x = -1.093282248Subproblem 2
x + 2.833333334 = -1.740051086 Simplifying x + 2.833333334 = -1.740051086 Reorder the terms: 2.833333334 + x = -1.740051086 Solving 2.833333334 + x = -1.740051086 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 = -1.740051086 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -1.740051086 + -2.833333334 x = -1.740051086 + -2.833333334 Combine like terms: -1.740051086 + -2.833333334 = -4.57338442 x = -4.57338442 Simplifying x = -4.57338442Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.093282248, -4.57338442}
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