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Simplifying 5X2 + 25X = -5 Reorder the terms: 25X + 5X2 = -5 Solving 25X + 5X2 = -5 Solving for variable 'X'. Reorder the terms: 5 + 25X + 5X2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 25X + 5X2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 5X + X2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 5X + X2)' equal to zero and attempt to solve: Simplifying 1 + 5X + X2 = 0 Solving 1 + 5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + 5X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5X + X2 = 0 + -1 5X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 5X + X2 = -1 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 = -1 + 6.25 Reorder the terms: 6.25 + 5X + X2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + 5X + X2 = 5.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (X + 2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
X + 2.5 = 2.291287847 Simplifying X + 2.5 = 2.291287847 Reorder the terms: 2.5 + X = 2.291287847 Solving 2.5 + X = 2.291287847 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 = 2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 2.291287847 + -2.5 X = 2.291287847 + -2.5 Combine like terms: 2.291287847 + -2.5 = -0.208712153 X = -0.208712153 Simplifying X = -0.208712153Subproblem 2
X + 2.5 = -2.291287847 Simplifying X + 2.5 = -2.291287847 Reorder the terms: 2.5 + X = -2.291287847 Solving 2.5 + X = -2.291287847 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 = -2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -2.291287847 + -2.5 X = -2.291287847 + -2.5 Combine like terms: -2.291287847 + -2.5 = -4.791287847 X = -4.791287847 Simplifying X = -4.791287847Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.208712153, -4.791287847}Solution
X = {-0.208712153, -4.791287847}
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