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Simplifying 17x2 + 4x + -20 = 0 Reorder the terms: -20 + 4x + 17x2 = 0 Solving -20 + 4x + 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'. -1.176470588 + 0.2352941176x + x2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + 0.2352941176x + 1.176470588 + x2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + 0.2352941176x + x2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + 0.2352941176x + x2 = 0 + 1.176470588 0.2352941176x + x2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 0.2352941176x + x2 = 1.176470588 The x term is 0.2352941176x. Take half its coefficient (0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. 0.2352941176x + 0.01384083044 + x2 = 1.176470588 + 0.01384083044 Reorder the terms: 0.01384083044 + 0.2352941176x + x2 = 1.176470588 + 0.01384083044 Combine like terms: 1.176470588 + 0.01384083044 = 1.19031141844 0.01384083044 + 0.2352941176x + x2 = 1.19031141844 Factor a perfect square on the left side: (x + 0.1176470588)(x + 0.1176470588) = 1.19031141844 Calculate the square root of the right side: 1.091013941 Break this problem into two subproblems by setting (x + 0.1176470588) equal to 1.091013941 and -1.091013941.Subproblem 1
x + 0.1176470588 = 1.091013941 Simplifying x + 0.1176470588 = 1.091013941 Reorder the terms: 0.1176470588 + x = 1.091013941 Solving 0.1176470588 + x = 1.091013941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = 1.091013941 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = 1.091013941 + -0.1176470588 x = 1.091013941 + -0.1176470588 Combine like terms: 1.091013941 + -0.1176470588 = 0.9733668822 x = 0.9733668822 Simplifying x = 0.9733668822Subproblem 2
x + 0.1176470588 = -1.091013941 Simplifying x + 0.1176470588 = -1.091013941 Reorder the terms: 0.1176470588 + x = -1.091013941 Solving 0.1176470588 + x = -1.091013941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = -1.091013941 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = -1.091013941 + -0.1176470588 x = -1.091013941 + -0.1176470588 Combine like terms: -1.091013941 + -0.1176470588 = -1.2086609998 x = -1.2086609998 Simplifying x = -1.2086609998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9733668822, -1.2086609998}
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