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Simplifying 5x2 + 25x + 3 = 0 Reorder the terms: 3 + 25x + 5x2 = 0 Solving 3 + 25x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 5x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 5x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 5x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 5x + x2 = 0 + -0.6 5x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 5x + x2 = -0.6 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 = -0.6 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.6 + 6.25 Combine like terms: -0.6 + 6.25 = 5.65 6.25 + 5x + x2 = 5.65 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5.65 Calculate the square root of the right side: 2.376972865 Break this problem into two subproblems by setting (x + 2.5) equal to 2.376972865 and -2.376972865.Subproblem 1
x + 2.5 = 2.376972865 Simplifying x + 2.5 = 2.376972865 Reorder the terms: 2.5 + x = 2.376972865 Solving 2.5 + x = 2.376972865 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 = 2.376972865 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.376972865 + -2.5 x = 2.376972865 + -2.5 Combine like terms: 2.376972865 + -2.5 = -0.123027135 x = -0.123027135 Simplifying x = -0.123027135Subproblem 2
x + 2.5 = -2.376972865 Simplifying x + 2.5 = -2.376972865 Reorder the terms: 2.5 + x = -2.376972865 Solving 2.5 + x = -2.376972865 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 = -2.376972865 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.376972865 + -2.5 x = -2.376972865 + -2.5 Combine like terms: -2.376972865 + -2.5 = -4.876972865 x = -4.876972865 Simplifying x = -4.876972865Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.123027135, -4.876972865}
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