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Simplifying 50x2 + 88x + 6 = 0 Reorder the terms: 6 + 88x + 50x2 = 0 Solving 6 + 88x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 44x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 44x + 25x2)' equal to zero and attempt to solve: Simplifying 3 + 44x + 25x2 = 0 Solving 3 + 44x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + 1.76x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + 1.76x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + 1.76x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + 1.76x + x2 = 0 + -0.12 1.76x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 1.76x + x2 = -0.12 The x term is 1.76x. Take half its coefficient (0.88). Square it (0.7744) and add it to both sides. Add '0.7744' to each side of the equation. 1.76x + 0.7744 + x2 = -0.12 + 0.7744 Reorder the terms: 0.7744 + 1.76x + x2 = -0.12 + 0.7744 Combine like terms: -0.12 + 0.7744 = 0.6544 0.7744 + 1.76x + x2 = 0.6544 Factor a perfect square on the left side: (x + 0.88)(x + 0.88) = 0.6544 Calculate the square root of the right side: 0.808949937 Break this problem into two subproblems by setting (x + 0.88) equal to 0.808949937 and -0.808949937.Subproblem 1
x + 0.88 = 0.808949937 Simplifying x + 0.88 = 0.808949937 Reorder the terms: 0.88 + x = 0.808949937 Solving 0.88 + x = 0.808949937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.88' to each side of the equation. 0.88 + -0.88 + x = 0.808949937 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 0.00 + x = 0.808949937 + -0.88 x = 0.808949937 + -0.88 Combine like terms: 0.808949937 + -0.88 = -0.071050063 x = -0.071050063 Simplifying x = -0.071050063Subproblem 2
x + 0.88 = -0.808949937 Simplifying x + 0.88 = -0.808949937 Reorder the terms: 0.88 + x = -0.808949937 Solving 0.88 + x = -0.808949937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.88' to each side of the equation. 0.88 + -0.88 + x = -0.808949937 + -0.88 Combine like terms: 0.88 + -0.88 = 0.00 0.00 + x = -0.808949937 + -0.88 x = -0.808949937 + -0.88 Combine like terms: -0.808949937 + -0.88 = -1.688949937 x = -1.688949937 Simplifying x = -1.688949937Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.071050063, -1.688949937}Solution
x = {-0.071050063, -1.688949937}
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