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Simplifying 5x2 + 25x + 4 = 2 Reorder the terms: 4 + 25x + 5x2 = 2 Solving 4 + 25x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: 4 + -2 + 25x + 5x2 = 2 + -2 Combine like terms: 4 + -2 = 2 2 + 25x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 2 + 25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 5x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 5x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 5x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 5x + x2 = 0 + -0.4 5x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 5x + x2 = -0.4 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -0.4 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.4 + 6.25 Combine like terms: -0.4 + 6.25 = 5.85 6.25 + 5x + x2 = 5.85 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5.85 Calculate the square root of the right side: 2.418677324 Break this problem into two subproblems by setting (x + 2.5) equal to 2.418677324 and -2.418677324.Subproblem 1
x + 2.5 = 2.418677324 Simplifying x + 2.5 = 2.418677324 Reorder the terms: 2.5 + x = 2.418677324 Solving 2.5 + x = 2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.418677324 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.418677324 + -2.5 x = 2.418677324 + -2.5 Combine like terms: 2.418677324 + -2.5 = -0.081322676 x = -0.081322676 Simplifying x = -0.081322676Subproblem 2
x + 2.5 = -2.418677324 Simplifying x + 2.5 = -2.418677324 Reorder the terms: 2.5 + x = -2.418677324 Solving 2.5 + x = -2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.418677324 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.418677324 + -2.5 x = -2.418677324 + -2.5 Combine like terms: -2.418677324 + -2.5 = -4.918677324 x = -4.918677324 Simplifying x = -4.918677324Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.081322676, -4.918677324}
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