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Simplifying 5x2 + 16 + -14 = 22 + -8x Reorder the terms: 16 + -14 + 5x2 = 22 + -8x Combine like terms: 16 + -14 = 2 2 + 5x2 = 22 + -8x Solving 2 + 5x2 = 22 + -8x Solving for variable 'x'. Reorder the terms: 2 + -22 + 8x + 5x2 = 22 + -8x + -22 + 8x Combine like terms: 2 + -22 = -20 -20 + 8x + 5x2 = 22 + -8x + -22 + 8x Reorder the terms: -20 + 8x + 5x2 = 22 + -22 + -8x + 8x Combine like terms: 22 + -22 = 0 -20 + 8x + 5x2 = 0 + -8x + 8x -20 + 8x + 5x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -20 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 1.6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.6x + x2 = 0 + 4 1.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.6x + x2 = 4 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 4 + 0.64 Combine like terms: 4 + 0.64 = 4.64 0.64 + 1.6x + x2 = 4.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + 0.8) equal to 2.154065923 and -2.154065923.Subproblem 1
x + 0.8 = 2.154065923 Simplifying x + 0.8 = 2.154065923 Reorder the terms: 0.8 + x = 2.154065923 Solving 0.8 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.154065923 + -0.8 x = 2.154065923 + -0.8 Combine like terms: 2.154065923 + -0.8 = 1.354065923 x = 1.354065923 Simplifying x = 1.354065923Subproblem 2
x + 0.8 = -2.154065923 Simplifying x + 0.8 = -2.154065923 Reorder the terms: 0.8 + x = -2.154065923 Solving 0.8 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.154065923 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.154065923 + -0.8 x = -2.154065923 + -0.8 Combine like terms: -2.154065923 + -0.8 = -2.954065923 x = -2.954065923 Simplifying x = -2.954065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.354065923, -2.954065923}
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