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Simplifying x = 25x + 5x2 + 0.2 Reorder the terms: x = 0.2 + 25x + 5x2 Solving x = 0.2 + 25x + 5x2 Solving for variable 'x'. Reorder the terms: -0.2 + x + -25x + -5x2 = 0.2 + 25x + 5x2 + -0.2 + -25x + -5x2 Combine like terms: x + -25x = -24x -0.2 + -24x + -5x2 = 0.2 + 25x + 5x2 + -0.2 + -25x + -5x2 Reorder the terms: -0.2 + -24x + -5x2 = 0.2 + -0.2 + 25x + -25x + 5x2 + -5x2 Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + -24x + -5x2 = 0.0 + 25x + -25x + 5x2 + -5x2 -0.2 + -24x + -5x2 = 25x + -25x + 5x2 + -5x2 Combine like terms: 25x + -25x = 0 -0.2 + -24x + -5x2 = 0 + 5x2 + -5x2 -0.2 + -24x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -0.2 + -24x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.04 + 4.8x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 4.8x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 4.8x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 4.8x + x2 = 0 + -0.04 4.8x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 4.8x + x2 = -0.04 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = -0.04 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = -0.04 + 5.76 Combine like terms: -0.04 + 5.76 = 5.72 5.76 + 4.8x + x2 = 5.72 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 5.72 Calculate the square root of the right side: 2.391652149 Break this problem into two subproblems by setting (x + 2.4) equal to 2.391652149 and -2.391652149.Subproblem 1
x + 2.4 = 2.391652149 Simplifying x + 2.4 = 2.391652149 Reorder the terms: 2.4 + x = 2.391652149 Solving 2.4 + x = 2.391652149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 2.391652149 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 2.391652149 + -2.4 x = 2.391652149 + -2.4 Combine like terms: 2.391652149 + -2.4 = -0.008347851 x = -0.008347851 Simplifying x = -0.008347851Subproblem 2
x + 2.4 = -2.391652149 Simplifying x + 2.4 = -2.391652149 Reorder the terms: 2.4 + x = -2.391652149 Solving 2.4 + x = -2.391652149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -2.391652149 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -2.391652149 + -2.4 x = -2.391652149 + -2.4 Combine like terms: -2.391652149 + -2.4 = -4.791652149 x = -4.791652149 Simplifying x = -4.791652149Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008347851, -4.791652149}
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