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Simplifying 5x2 + -20x + -31 = 0 Reorder the terms: -31 + -20x + 5x2 = 0 Solving -31 + -20x + 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'. -6.2 + -4x + x2 = 0 Move the constant term to the right: Add '6.2' to each side of the equation. -6.2 + -4x + 6.2 + x2 = 0 + 6.2 Reorder the terms: -6.2 + 6.2 + -4x + x2 = 0 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + -4x + x2 = 0 + 6.2 -4x + x2 = 0 + 6.2 Combine like terms: 0 + 6.2 = 6.2 -4x + x2 = 6.2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6.2 + 4 Reorder the terms: 4 + -4x + x2 = 6.2 + 4 Combine like terms: 6.2 + 4 = 10.2 4 + -4x + x2 = 10.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 10.2 Calculate the square root of the right side: 3.193743885 Break this problem into two subproblems by setting (x + -2) equal to 3.193743885 and -3.193743885.Subproblem 1
x + -2 = 3.193743885 Simplifying x + -2 = 3.193743885 Reorder the terms: -2 + x = 3.193743885 Solving -2 + x = 3.193743885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.193743885 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.193743885 + 2 x = 3.193743885 + 2 Combine like terms: 3.193743885 + 2 = 5.193743885 x = 5.193743885 Simplifying x = 5.193743885Subproblem 2
x + -2 = -3.193743885 Simplifying x + -2 = -3.193743885 Reorder the terms: -2 + x = -3.193743885 Solving -2 + x = -3.193743885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.193743885 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.193743885 + 2 x = -3.193743885 + 2 Combine like terms: -3.193743885 + 2 = -1.193743885 x = -1.193743885 Simplifying x = -1.193743885Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.193743885, -1.193743885}
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