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Simplifying 5x2 + -20x = 11 Reorder the terms: -20x + 5x2 = 11 Solving -20x + 5x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -20x + 5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -4x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -4x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -4x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -4x + x2 = 0 + 2.2 -4x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -4x + x2 = 2.2 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 = 2.2 + 4 Reorder the terms: 4 + -4x + x2 = 2.2 + 4 Combine like terms: 2.2 + 4 = 6.2 4 + -4x + x2 = 6.2 Factor a perfect square on the left side: (x + -2)(x + -2) = 6.2 Calculate the square root of the right side: 2.48997992 Break this problem into two subproblems by setting (x + -2) equal to 2.48997992 and -2.48997992.Subproblem 1
x + -2 = 2.48997992 Simplifying x + -2 = 2.48997992 Reorder the terms: -2 + x = 2.48997992 Solving -2 + x = 2.48997992 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 = 2.48997992 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.48997992 + 2 x = 2.48997992 + 2 Combine like terms: 2.48997992 + 2 = 4.48997992 x = 4.48997992 Simplifying x = 4.48997992Subproblem 2
x + -2 = -2.48997992 Simplifying x + -2 = -2.48997992 Reorder the terms: -2 + x = -2.48997992 Solving -2 + x = -2.48997992 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 = -2.48997992 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.48997992 + 2 x = -2.48997992 + 2 Combine like terms: -2.48997992 + 2 = -0.48997992 x = -0.48997992 Simplifying x = -0.48997992Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.48997992, -0.48997992}
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