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Simplifying 17x2 + -20x + -24 = 0 Reorder the terms: -24 + -20x + 17x2 = 0 Solving -24 + -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'. -1.411764706 + -1.176470588x + x2 = 0 Move the constant term to the right: Add '1.411764706' to each side of the equation. -1.411764706 + -1.176470588x + 1.411764706 + x2 = 0 + 1.411764706 Reorder the terms: -1.411764706 + 1.411764706 + -1.176470588x + x2 = 0 + 1.411764706 Combine like terms: -1.411764706 + 1.411764706 = 0.000000000 0.000000000 + -1.176470588x + x2 = 0 + 1.411764706 -1.176470588x + x2 = 0 + 1.411764706 Combine like terms: 0 + 1.411764706 = 1.411764706 -1.176470588x + x2 = 1.411764706 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 = 1.411764706 + 0.3460207611 Reorder the terms: 0.3460207611 + -1.176470588x + x2 = 1.411764706 + 0.3460207611 Combine like terms: 1.411764706 + 0.3460207611 = 1.7577854671 0.3460207611 + -1.176470588x + x2 = 1.7577854671 Factor a perfect square on the left side: (x + -0.588235294)(x + -0.588235294) = 1.7577854671 Calculate the square root of the right side: 1.32581502 Break this problem into two subproblems by setting (x + -0.588235294) equal to 1.32581502 and -1.32581502.Subproblem 1
x + -0.588235294 = 1.32581502 Simplifying x + -0.588235294 = 1.32581502 Reorder the terms: -0.588235294 + x = 1.32581502 Solving -0.588235294 + x = 1.32581502 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 = 1.32581502 + 0.588235294 Combine like terms: -0.588235294 + 0.588235294 = 0.000000000 0.000000000 + x = 1.32581502 + 0.588235294 x = 1.32581502 + 0.588235294 Combine like terms: 1.32581502 + 0.588235294 = 1.914050314 x = 1.914050314 Simplifying x = 1.914050314Subproblem 2
x + -0.588235294 = -1.32581502 Simplifying x + -0.588235294 = -1.32581502 Reorder the terms: -0.588235294 + x = -1.32581502 Solving -0.588235294 + x = -1.32581502 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 = -1.32581502 + 0.588235294 Combine like terms: -0.588235294 + 0.588235294 = 0.000000000 0.000000000 + x = -1.32581502 + 0.588235294 x = -1.32581502 + 0.588235294 Combine like terms: -1.32581502 + 0.588235294 = -0.737579726 x = -0.737579726 Simplifying x = -0.737579726Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.914050314, -0.737579726}
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