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Simplifying 17x2 + 12x + -2 = 0 Reorder the terms: -2 + 12x + 17x2 = 0 Solving -2 + 12x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.1176470588 + 0.7058823529x + x2 = 0 Move the constant term to the right: Add '0.1176470588' to each side of the equation. -0.1176470588 + 0.7058823529x + 0.1176470588 + x2 = 0 + 0.1176470588 Reorder the terms: -0.1176470588 + 0.1176470588 + 0.7058823529x + x2 = 0 + 0.1176470588 Combine like terms: -0.1176470588 + 0.1176470588 = 0.0000000000 0.0000000000 + 0.7058823529x + x2 = 0 + 0.1176470588 0.7058823529x + x2 = 0 + 0.1176470588 Combine like terms: 0 + 0.1176470588 = 0.1176470588 0.7058823529x + x2 = 0.1176470588 The x term is 0.7058823529x. Take half its coefficient (0.3529411765). Square it (0.1245674741) and add it to both sides. Add '0.1245674741' to each side of the equation. 0.7058823529x + 0.1245674741 + x2 = 0.1176470588 + 0.1245674741 Reorder the terms: 0.1245674741 + 0.7058823529x + x2 = 0.1176470588 + 0.1245674741 Combine like terms: 0.1176470588 + 0.1245674741 = 0.2422145329 0.1245674741 + 0.7058823529x + x2 = 0.2422145329 Factor a perfect square on the left side: (x + 0.3529411765)(x + 0.3529411765) = 0.2422145329 Calculate the square root of the right side: 0.492152957 Break this problem into two subproblems by setting (x + 0.3529411765) equal to 0.492152957 and -0.492152957.Subproblem 1
x + 0.3529411765 = 0.492152957 Simplifying x + 0.3529411765 = 0.492152957 Reorder the terms: 0.3529411765 + x = 0.492152957 Solving 0.3529411765 + x = 0.492152957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3529411765' to each side of the equation. 0.3529411765 + -0.3529411765 + x = 0.492152957 + -0.3529411765 Combine like terms: 0.3529411765 + -0.3529411765 = 0.0000000000 0.0000000000 + x = 0.492152957 + -0.3529411765 x = 0.492152957 + -0.3529411765 Combine like terms: 0.492152957 + -0.3529411765 = 0.1392117805 x = 0.1392117805 Simplifying x = 0.1392117805Subproblem 2
x + 0.3529411765 = -0.492152957 Simplifying x + 0.3529411765 = -0.492152957 Reorder the terms: 0.3529411765 + x = -0.492152957 Solving 0.3529411765 + x = -0.492152957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3529411765' to each side of the equation. 0.3529411765 + -0.3529411765 + x = -0.492152957 + -0.3529411765 Combine like terms: 0.3529411765 + -0.3529411765 = 0.0000000000 0.0000000000 + x = -0.492152957 + -0.3529411765 x = -0.492152957 + -0.3529411765 Combine like terms: -0.492152957 + -0.3529411765 = -0.8450941335 x = -0.8450941335 Simplifying x = -0.8450941335Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1392117805, -0.8450941335}
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