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Simplifying 3x2 + 17x + 6 = 180 Reorder the terms: 6 + 17x + 3x2 = 180 Solving 6 + 17x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + 17x + 3x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + 17x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -58 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '58' to each side of the equation. -58 + 5.666666667x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 5.666666667x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 5.666666667x + x2 = 0 + 58 5.666666667x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 5.666666667x + x2 = 58 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 = 58 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 58 + 8.027777782 Combine like terms: 58 + 8.027777782 = 66.027777782 8.027777782 + 5.666666667x + x2 = 66.027777782 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 66.027777782 Calculate the square root of the right side: 8.125747829 Break this problem into two subproblems by setting (x + 2.833333334) equal to 8.125747829 and -8.125747829.Subproblem 1
x + 2.833333334 = 8.125747829 Simplifying x + 2.833333334 = 8.125747829 Reorder the terms: 2.833333334 + x = 8.125747829 Solving 2.833333334 + x = 8.125747829 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 = 8.125747829 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 8.125747829 + -2.833333334 x = 8.125747829 + -2.833333334 Combine like terms: 8.125747829 + -2.833333334 = 5.292414495 x = 5.292414495 Simplifying x = 5.292414495Subproblem 2
x + 2.833333334 = -8.125747829 Simplifying x + 2.833333334 = -8.125747829 Reorder the terms: 2.833333334 + x = -8.125747829 Solving 2.833333334 + x = -8.125747829 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 = -8.125747829 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -8.125747829 + -2.833333334 x = -8.125747829 + -2.833333334 Combine like terms: -8.125747829 + -2.833333334 = -10.959081163 x = -10.959081163 Simplifying x = -10.959081163Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.292414495, -10.959081163}
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