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Simplifying 5x2 + -34x + -1 = 0 Reorder the terms: -1 + -34x + 5x2 = 0 Solving -1 + -34x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -6.8x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -6.8x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -6.8x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -6.8x + x2 = 0 + 0.2 -6.8x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -6.8x + x2 = 0.2 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = 0.2 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = 0.2 + 11.56 Combine like terms: 0.2 + 11.56 = 11.76 11.56 + -6.8x + x2 = 11.76 Factor a perfect square on the left side: (x + -3.4)(x + -3.4) = 11.76 Calculate the square root of the right side: 3.42928564 Break this problem into two subproblems by setting (x + -3.4) equal to 3.42928564 and -3.42928564.Subproblem 1
x + -3.4 = 3.42928564 Simplifying x + -3.4 = 3.42928564 Reorder the terms: -3.4 + x = 3.42928564 Solving -3.4 + x = 3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 3.42928564 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 3.42928564 + 3.4 x = 3.42928564 + 3.4 Combine like terms: 3.42928564 + 3.4 = 6.82928564 x = 6.82928564 Simplifying x = 6.82928564Subproblem 2
x + -3.4 = -3.42928564 Simplifying x + -3.4 = -3.42928564 Reorder the terms: -3.4 + x = -3.42928564 Solving -3.4 + x = -3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -3.42928564 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -3.42928564 + 3.4 x = -3.42928564 + 3.4 Combine like terms: -3.42928564 + 3.4 = -0.02928564 x = -0.02928564 Simplifying x = -0.02928564Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.82928564, -0.02928564}
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