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Simplifying 0 = 5x2 + 25x + 4 Reorder the terms: 0 = 4 + 25x + 5x2 Solving 0 = 4 + 25x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -25x + -5x2 = 4 + 25x + 5x2 + -4 + -25x + -5x2 Reorder the terms: -4 + -25x + -5x2 = 4 + -4 + 25x + -25x + 5x2 + -5x2 Combine like terms: 4 + -4 = 0 -4 + -25x + -5x2 = 0 + 25x + -25x + 5x2 + -5x2 -4 + -25x + -5x2 = 25x + -25x + 5x2 + -5x2 Combine like terms: 25x + -25x = 0 -4 + -25x + -5x2 = 0 + 5x2 + -5x2 -4 + -25x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -4 + -25x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 25x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 25x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 25x + 5x2 = 0 Solving 4 + 25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 5x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 5x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 5x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 5x + x2 = 0 + -0.8 5x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 5x + x2 = -0.8 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 = -0.8 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -0.8 + 6.25 Combine like terms: -0.8 + 6.25 = 5.45 6.25 + 5x + x2 = 5.45 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5.45 Calculate the square root of the right side: 2.334523506 Break this problem into two subproblems by setting (x + 2.5) equal to 2.334523506 and -2.334523506.Subproblem 1
x + 2.5 = 2.334523506 Simplifying x + 2.5 = 2.334523506 Reorder the terms: 2.5 + x = 2.334523506 Solving 2.5 + x = 2.334523506 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 = 2.334523506 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.334523506 + -2.5 x = 2.334523506 + -2.5 Combine like terms: 2.334523506 + -2.5 = -0.165476494 x = -0.165476494 Simplifying x = -0.165476494Subproblem 2
x + 2.5 = -2.334523506 Simplifying x + 2.5 = -2.334523506 Reorder the terms: 2.5 + x = -2.334523506 Solving 2.5 + x = -2.334523506 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 = -2.334523506 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.334523506 + -2.5 x = -2.334523506 + -2.5 Combine like terms: -2.334523506 + -2.5 = -4.834523506 x = -4.834523506 Simplifying x = -4.834523506Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.165476494, -4.834523506}Solution
x = {-0.165476494, -4.834523506}
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