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Simplifying 5x2 + -20x + -20 = 16x + -4x2 Reorder the terms: -20 + -20x + 5x2 = 16x + -4x2 Solving -20 + -20x + 5x2 = 16x + -4x2 Solving for variable 'x'. Reorder the terms: -20 + -20x + -16x + 5x2 + 4x2 = 16x + -4x2 + -16x + 4x2 Combine like terms: -20x + -16x = -36x -20 + -36x + 5x2 + 4x2 = 16x + -4x2 + -16x + 4x2 Combine like terms: 5x2 + 4x2 = 9x2 -20 + -36x + 9x2 = 16x + -4x2 + -16x + 4x2 Reorder the terms: -20 + -36x + 9x2 = 16x + -16x + -4x2 + 4x2 Combine like terms: 16x + -16x = 0 -20 + -36x + 9x2 = 0 + -4x2 + 4x2 -20 + -36x + 9x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -20 + -36x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -4x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -4x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -4x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -4x + x2 = 0 + 2.222222222 -4x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -4x + x2 = 2.222222222 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 = 2.222222222 + 4 Reorder the terms: 4 + -4x + x2 = 2.222222222 + 4 Combine like terms: 2.222222222 + 4 = 6.222222222 4 + -4x + x2 = 6.222222222 Factor a perfect square on the left side: (x + -2)(x + -2) = 6.222222222 Calculate the square root of the right side: 2.494438258 Break this problem into two subproblems by setting (x + -2) equal to 2.494438258 and -2.494438258.Subproblem 1
x + -2 = 2.494438258 Simplifying x + -2 = 2.494438258 Reorder the terms: -2 + x = 2.494438258 Solving -2 + x = 2.494438258 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 = 2.494438258 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.494438258 + 2 x = 2.494438258 + 2 Combine like terms: 2.494438258 + 2 = 4.494438258 x = 4.494438258 Simplifying x = 4.494438258Subproblem 2
x + -2 = -2.494438258 Simplifying x + -2 = -2.494438258 Reorder the terms: -2 + x = -2.494438258 Solving -2 + x = -2.494438258 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 = -2.494438258 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.494438258 + 2 x = -2.494438258 + 2 Combine like terms: -2.494438258 + 2 = -0.494438258 x = -0.494438258 Simplifying x = -0.494438258Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.494438258, -0.494438258}
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