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Simplifying -17x2 + -30x + -1 = 0 Reorder the terms: -1 + -30x + -17x2 = 0 Solving -1 + -30x + -17x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 30x + 17x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 30x + 17x2)' equal to zero and attempt to solve: Simplifying 1 + 30x + 17x2 = 0 Solving 1 + 30x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.05882352941 + 1.764705882x + x2 = 0 Move the constant term to the right: Add '-0.05882352941' to each side of the equation. 0.05882352941 + 1.764705882x + -0.05882352941 + x2 = 0 + -0.05882352941 Reorder the terms: 0.05882352941 + -0.05882352941 + 1.764705882x + x2 = 0 + -0.05882352941 Combine like terms: 0.05882352941 + -0.05882352941 = 0.00000000000 0.00000000000 + 1.764705882x + x2 = 0 + -0.05882352941 1.764705882x + x2 = 0 + -0.05882352941 Combine like terms: 0 + -0.05882352941 = -0.05882352941 1.764705882x + x2 = -0.05882352941 The x term is 1.764705882x. Take half its coefficient (0.882352941). Square it (0.7785467125) and add it to both sides. Add '0.7785467125' to each side of the equation. 1.764705882x + 0.7785467125 + x2 = -0.05882352941 + 0.7785467125 Reorder the terms: 0.7785467125 + 1.764705882x + x2 = -0.05882352941 + 0.7785467125 Combine like terms: -0.05882352941 + 0.7785467125 = 0.71972318309 0.7785467125 + 1.764705882x + x2 = 0.71972318309 Factor a perfect square on the left side: (x + 0.882352941)(x + 0.882352941) = 0.71972318309 Calculate the square root of the right side: 0.848365006 Break this problem into two subproblems by setting (x + 0.882352941) equal to 0.848365006 and -0.848365006.Subproblem 1
x + 0.882352941 = 0.848365006 Simplifying x + 0.882352941 = 0.848365006 Reorder the terms: 0.882352941 + x = 0.848365006 Solving 0.882352941 + x = 0.848365006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.882352941' to each side of the equation. 0.882352941 + -0.882352941 + x = 0.848365006 + -0.882352941 Combine like terms: 0.882352941 + -0.882352941 = 0.000000000 0.000000000 + x = 0.848365006 + -0.882352941 x = 0.848365006 + -0.882352941 Combine like terms: 0.848365006 + -0.882352941 = -0.033987935 x = -0.033987935 Simplifying x = -0.033987935Subproblem 2
x + 0.882352941 = -0.848365006 Simplifying x + 0.882352941 = -0.848365006 Reorder the terms: 0.882352941 + x = -0.848365006 Solving 0.882352941 + x = -0.848365006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.882352941' to each side of the equation. 0.882352941 + -0.882352941 + x = -0.848365006 + -0.882352941 Combine like terms: 0.882352941 + -0.882352941 = 0.000000000 0.000000000 + x = -0.848365006 + -0.882352941 x = -0.848365006 + -0.882352941 Combine like terms: -0.848365006 + -0.882352941 = -1.730717947 x = -1.730717947 Simplifying x = -1.730717947Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.033987935, -1.730717947}Solution
x = {-0.033987935, -1.730717947}
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