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Simplifying 50x2 + 118x = -2 Reorder the terms: 118x + 50x2 = -2 Solving 118x + 50x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 118x + 50x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 118x + 50x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 59x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 59x + 25x2)' equal to zero and attempt to solve: Simplifying 1 + 59x + 25x2 = 0 Solving 1 + 59x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.04 + 2.36x + x2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 2.36x + -0.04 + x2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 2.36x + x2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 2.36x + x2 = 0 + -0.04 2.36x + x2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 2.36x + x2 = -0.04 The x term is 2.36x. Take half its coefficient (1.18). Square it (1.3924) and add it to both sides. Add '1.3924' to each side of the equation. 2.36x + 1.3924 + x2 = -0.04 + 1.3924 Reorder the terms: 1.3924 + 2.36x + x2 = -0.04 + 1.3924 Combine like terms: -0.04 + 1.3924 = 1.3524 1.3924 + 2.36x + x2 = 1.3524 Factor a perfect square on the left side: (x + 1.18)(x + 1.18) = 1.3524 Calculate the square root of the right side: 1.162927341 Break this problem into two subproblems by setting (x + 1.18) equal to 1.162927341 and -1.162927341.Subproblem 1
x + 1.18 = 1.162927341 Simplifying x + 1.18 = 1.162927341 Reorder the terms: 1.18 + x = 1.162927341 Solving 1.18 + x = 1.162927341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.18' to each side of the equation. 1.18 + -1.18 + x = 1.162927341 + -1.18 Combine like terms: 1.18 + -1.18 = 0.00 0.00 + x = 1.162927341 + -1.18 x = 1.162927341 + -1.18 Combine like terms: 1.162927341 + -1.18 = -0.017072659 x = -0.017072659 Simplifying x = -0.017072659Subproblem 2
x + 1.18 = -1.162927341 Simplifying x + 1.18 = -1.162927341 Reorder the terms: 1.18 + x = -1.162927341 Solving 1.18 + x = -1.162927341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.18' to each side of the equation. 1.18 + -1.18 + x = -1.162927341 + -1.18 Combine like terms: 1.18 + -1.18 = 0.00 0.00 + x = -1.162927341 + -1.18 x = -1.162927341 + -1.18 Combine like terms: -1.162927341 + -1.18 = -2.342927341 x = -2.342927341 Simplifying x = -2.342927341Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.017072659, -2.342927341}Solution
x = {-0.017072659, -2.342927341}
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