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Simplifying -17x2 + -2x + 20 = 0 Reorder the terms: 20 + -2x + -17x2 = 0 Solving 20 + -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'. -1.176470588 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + 0.1176470588x + 1.176470588 + x2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + 0.1176470588x + x2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + 0.1176470588x + x2 = 0 + 1.176470588 0.1176470588x + x2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 0.1176470588x + x2 = 1.176470588 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 = 1.176470588 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 1.176470588 + 0.003460207611 Combine like terms: 1.176470588 + 0.003460207611 = 1.179930795611 0.003460207611 + 0.1176470588x + x2 = 1.179930795611 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 1.179930795611 Calculate the square root of the right side: 1.086246195 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 1.086246195 and -1.086246195.Subproblem 1
x + 0.0588235294 = 1.086246195 Simplifying x + 0.0588235294 = 1.086246195 Reorder the terms: 0.0588235294 + x = 1.086246195 Solving 0.0588235294 + x = 1.086246195 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 = 1.086246195 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 1.086246195 + -0.0588235294 x = 1.086246195 + -0.0588235294 Combine like terms: 1.086246195 + -0.0588235294 = 1.0274226656 x = 1.0274226656 Simplifying x = 1.0274226656Subproblem 2
x + 0.0588235294 = -1.086246195 Simplifying x + 0.0588235294 = -1.086246195 Reorder the terms: 0.0588235294 + x = -1.086246195 Solving 0.0588235294 + x = -1.086246195 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 = -1.086246195 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -1.086246195 + -0.0588235294 x = -1.086246195 + -0.0588235294 Combine like terms: -1.086246195 + -0.0588235294 = -1.1450697244 x = -1.1450697244 Simplifying x = -1.1450697244Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0274226656, -1.1450697244}
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