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Simplifying 20x2 + 4 = 25x2 + 5x Reorder the terms: 4 + 20x2 = 25x2 + 5x Reorder the terms: 4 + 20x2 = 5x + 25x2 Solving 4 + 20x2 = 5x + 25x2 Solving for variable 'x'. Reorder the terms: 4 + -5x + 20x2 + -25x2 = 5x + 25x2 + -5x + -25x2 Combine like terms: 20x2 + -25x2 = -5x2 4 + -5x + -5x2 = 5x + 25x2 + -5x + -25x2 Reorder the terms: 4 + -5x + -5x2 = 5x + -5x + 25x2 + -25x2 Combine like terms: 5x + -5x = 0 4 + -5x + -5x2 = 0 + 25x2 + -25x2 4 + -5x + -5x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 4 + -5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x + x2 = 0 + 0.8 x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 x + x2 = 0.8 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.8 + 0.25 Combine like terms: 0.8 + 0.25 = 1.05 1.25 + x2 = 1.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + 0.5) equal to 1.024695077 and -1.024695077.Subproblem 1
x + 0.5 = 1.024695077 Simplifying x + 0.5 = 1.024695077 Reorder the terms: 0.5 + x = 1.024695077 Solving 0.5 + x = 1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.024695077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.024695077 + -0.5 x = 1.024695077 + -0.5 Combine like terms: 1.024695077 + -0.5 = 0.524695077 x = 0.524695077 Simplifying x = 0.524695077Subproblem 2
x + 0.5 = -1.024695077 Simplifying x + 0.5 = -1.024695077 Reorder the terms: 0.5 + x = -1.024695077 Solving 0.5 + x = -1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.024695077 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.024695077 + -0.5 x = -1.024695077 + -0.5 Combine like terms: -1.024695077 + -0.5 = -1.524695077 x = -1.524695077 Simplifying x = -1.524695077Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.524695077, -1.524695077}
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