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Simplifying 50x2 + -75x + -1 = 0 Reorder the terms: -1 + -75x + 50x2 = 0 Solving -1 + -75x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.02 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + -1.5x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + -1.5x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + -1.5x + x2 = 0 + 0.02 -1.5x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 -1.5x + x2 = 0.02 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.02 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.02 + 0.5625 Combine like terms: 0.02 + 0.5625 = 0.5825 0.5625 + -1.5x + x2 = 0.5825 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.5825 Calculate the square root of the right side: 0.763216876 Break this problem into two subproblems by setting (x + -0.75) equal to 0.763216876 and -0.763216876.Subproblem 1
x + -0.75 = 0.763216876 Simplifying x + -0.75 = 0.763216876 Reorder the terms: -0.75 + x = 0.763216876 Solving -0.75 + x = 0.763216876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.763216876 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.763216876 + 0.75 x = 0.763216876 + 0.75 Combine like terms: 0.763216876 + 0.75 = 1.513216876 x = 1.513216876 Simplifying x = 1.513216876Subproblem 2
x + -0.75 = -0.763216876 Simplifying x + -0.75 = -0.763216876 Reorder the terms: -0.75 + x = -0.763216876 Solving -0.75 + x = -0.763216876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.763216876 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.763216876 + 0.75 x = -0.763216876 + 0.75 Combine like terms: -0.763216876 + 0.75 = -0.013216876 x = -0.013216876 Simplifying x = -0.013216876Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.513216876, -0.013216876}
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