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Simplifying 17x2 + 2x + -13 = 0 Reorder the terms: -13 + 2x + 17x2 = 0 Solving -13 + 2x + 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'. -0.7647058824 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '0.7647058824' to each side of the equation. -0.7647058824 + 0.1176470588x + 0.7647058824 + x2 = 0 + 0.7647058824 Reorder the terms: -0.7647058824 + 0.7647058824 + 0.1176470588x + x2 = 0 + 0.7647058824 Combine like terms: -0.7647058824 + 0.7647058824 = 0.0000000000 0.0000000000 + 0.1176470588x + x2 = 0 + 0.7647058824 0.1176470588x + x2 = 0 + 0.7647058824 Combine like terms: 0 + 0.7647058824 = 0.7647058824 0.1176470588x + x2 = 0.7647058824 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 0.7647058824 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 0.7647058824 + 0.003460207611 Combine like terms: 0.7647058824 + 0.003460207611 = 0.768166090011 0.003460207611 + 0.1176470588x + x2 = 0.768166090011 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 0.768166090011 Calculate the square root of the right side: 0.876450849 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 0.876450849 and -0.876450849.Subproblem 1
x + 0.0588235294 = 0.876450849 Simplifying x + 0.0588235294 = 0.876450849 Reorder the terms: 0.0588235294 + x = 0.876450849 Solving 0.0588235294 + x = 0.876450849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 0.876450849 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 0.876450849 + -0.0588235294 x = 0.876450849 + -0.0588235294 Combine like terms: 0.876450849 + -0.0588235294 = 0.8176273196 x = 0.8176273196 Simplifying x = 0.8176273196Subproblem 2
x + 0.0588235294 = -0.876450849 Simplifying x + 0.0588235294 = -0.876450849 Reorder the terms: 0.0588235294 + x = -0.876450849 Solving 0.0588235294 + x = -0.876450849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -0.876450849 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -0.876450849 + -0.0588235294 x = -0.876450849 + -0.0588235294 Combine like terms: -0.876450849 + -0.0588235294 = -0.9352743784 x = -0.9352743784 Simplifying x = -0.9352743784Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8176273196, -0.9352743784}
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