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Simplifying 0 = 5x2 + 50x + 1 Reorder the terms: 0 = 1 + 50x + 5x2 Solving 0 = 1 + 50x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -50x + -5x2 = 1 + 50x + 5x2 + -1 + -50x + -5x2 Reorder the terms: -1 + -50x + -5x2 = 1 + -1 + 50x + -50x + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 -1 + -50x + -5x2 = 0 + 50x + -50x + 5x2 + -5x2 -1 + -50x + -5x2 = 50x + -50x + 5x2 + -5x2 Combine like terms: 50x + -50x = 0 -1 + -50x + -5x2 = 0 + 5x2 + -5x2 -1 + -50x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -1 + -50x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 50x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 50x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 50x + 5x2 = 0 Solving 1 + 50x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 10x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 10x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 10x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 10x + x2 = 0 + -0.2 10x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 10x + x2 = -0.2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -0.2 + 25 Reorder the terms: 25 + 10x + x2 = -0.2 + 25 Combine like terms: -0.2 + 25 = 24.8 25 + 10x + x2 = 24.8 Factor a perfect square on the left side: (x + 5)(x + 5) = 24.8 Calculate the square root of the right side: 4.979959839 Break this problem into two subproblems by setting (x + 5) equal to 4.979959839 and -4.979959839.Subproblem 1
x + 5 = 4.979959839 Simplifying x + 5 = 4.979959839 Reorder the terms: 5 + x = 4.979959839 Solving 5 + x = 4.979959839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.979959839 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.979959839 + -5 x = 4.979959839 + -5 Combine like terms: 4.979959839 + -5 = -0.020040161 x = -0.020040161 Simplifying x = -0.020040161Subproblem 2
x + 5 = -4.979959839 Simplifying x + 5 = -4.979959839 Reorder the terms: 5 + x = -4.979959839 Solving 5 + x = -4.979959839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.979959839 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.979959839 + -5 x = -4.979959839 + -5 Combine like terms: -4.979959839 + -5 = -9.979959839 x = -9.979959839 Simplifying x = -9.979959839Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.020040161, -9.979959839}Solution
x = {-0.020040161, -9.979959839}
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