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Simplifying 5x2 + -180x + 4 = 0 Reorder the terms: 4 + -180x + 5x2 = 0 Solving 4 + -180x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -36x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -36x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -36x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -36x + x2 = 0 + -0.8 -36x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -36x + x2 = -0.8 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -0.8 + 324 Reorder the terms: 324 + -36x + x2 = -0.8 + 324 Combine like terms: -0.8 + 324 = 323.2 324 + -36x + x2 = 323.2 Factor a perfect square on the left side: (x + -18)(x + -18) = 323.2 Calculate the square root of the right side: 17.977764043 Break this problem into two subproblems by setting (x + -18) equal to 17.977764043 and -17.977764043.Subproblem 1
x + -18 = 17.977764043 Simplifying x + -18 = 17.977764043 Reorder the terms: -18 + x = 17.977764043 Solving -18 + x = 17.977764043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 17.977764043 + 18 Combine like terms: -18 + 18 = 0 0 + x = 17.977764043 + 18 x = 17.977764043 + 18 Combine like terms: 17.977764043 + 18 = 35.977764043 x = 35.977764043 Simplifying x = 35.977764043Subproblem 2
x + -18 = -17.977764043 Simplifying x + -18 = -17.977764043 Reorder the terms: -18 + x = -17.977764043 Solving -18 + x = -17.977764043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -17.977764043 + 18 Combine like terms: -18 + 18 = 0 0 + x = -17.977764043 + 18 x = -17.977764043 + 18 Combine like terms: -17.977764043 + 18 = 0.022235957 x = 0.022235957 Simplifying x = 0.022235957Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.977764043, 0.022235957}
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