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Simplifying 17x2 + 20x + -4 = 0 Reorder the terms: -4 + 20x + 17x2 = 0 Solving -4 + 20x + 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'. -0.2352941176 + 1.176470588x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + 1.176470588x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + 1.176470588x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + 1.176470588x + x2 = 0 + 0.2352941176 1.176470588x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 1.176470588x + x2 = 0.2352941176 The x term is 1.176470588x. Take half its coefficient (0.588235294). Square it (0.3460207611) and add it to both sides. Add '0.3460207611' to each side of the equation. 1.176470588x + 0.3460207611 + x2 = 0.2352941176 + 0.3460207611 Reorder the terms: 0.3460207611 + 1.176470588x + x2 = 0.2352941176 + 0.3460207611 Combine like terms: 0.2352941176 + 0.3460207611 = 0.5813148787 0.3460207611 + 1.176470588x + x2 = 0.5813148787 Factor a perfect square on the left side: (x + 0.588235294)(x + 0.588235294) = 0.5813148787 Calculate the square root of the right side: 0.762440082 Break this problem into two subproblems by setting (x + 0.588235294) equal to 0.762440082 and -0.762440082.Subproblem 1
x + 0.588235294 = 0.762440082 Simplifying x + 0.588235294 = 0.762440082 Reorder the terms: 0.588235294 + x = 0.762440082 Solving 0.588235294 + x = 0.762440082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.588235294' to each side of the equation. 0.588235294 + -0.588235294 + x = 0.762440082 + -0.588235294 Combine like terms: 0.588235294 + -0.588235294 = 0.000000000 0.000000000 + x = 0.762440082 + -0.588235294 x = 0.762440082 + -0.588235294 Combine like terms: 0.762440082 + -0.588235294 = 0.174204788 x = 0.174204788 Simplifying x = 0.174204788Subproblem 2
x + 0.588235294 = -0.762440082 Simplifying x + 0.588235294 = -0.762440082 Reorder the terms: 0.588235294 + x = -0.762440082 Solving 0.588235294 + x = -0.762440082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.588235294' to each side of the equation. 0.588235294 + -0.588235294 + x = -0.762440082 + -0.588235294 Combine like terms: 0.588235294 + -0.588235294 = 0.000000000 0.000000000 + x = -0.762440082 + -0.588235294 x = -0.762440082 + -0.588235294 Combine like terms: -0.762440082 + -0.588235294 = -1.350675376 x = -1.350675376 Simplifying x = -1.350675376Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.174204788, -1.350675376}
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