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Simplifying -145x2 + 36x + 4 = 0 Reorder the terms: 4 + 36x + -145x2 = 0 Solving 4 + 36x + -145x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -145 the coefficient of the squared term: Divide each side by '-145'. -0.0275862069 + -0.2482758621x + x2 = 0 Move the constant term to the right: Add '0.0275862069' to each side of the equation. -0.0275862069 + -0.2482758621x + 0.0275862069 + x2 = 0 + 0.0275862069 Reorder the terms: -0.0275862069 + 0.0275862069 + -0.2482758621x + x2 = 0 + 0.0275862069 Combine like terms: -0.0275862069 + 0.0275862069 = 0.0000000000 0.0000000000 + -0.2482758621x + x2 = 0 + 0.0275862069 -0.2482758621x + x2 = 0 + 0.0275862069 Combine like terms: 0 + 0.0275862069 = 0.0275862069 -0.2482758621x + x2 = 0.0275862069 The x term is -0.2482758621x. Take half its coefficient (-0.1241379311). Square it (0.01541022594) and add it to both sides. Add '0.01541022594' to each side of the equation. -0.2482758621x + 0.01541022594 + x2 = 0.0275862069 + 0.01541022594 Reorder the terms: 0.01541022594 + -0.2482758621x + x2 = 0.0275862069 + 0.01541022594 Combine like terms: 0.0275862069 + 0.01541022594 = 0.04299643284 0.01541022594 + -0.2482758621x + x2 = 0.04299643284 Factor a perfect square on the left side: (x + -0.1241379311)(x + -0.1241379311) = 0.04299643284 Calculate the square root of the right side: 0.207355812 Break this problem into two subproblems by setting (x + -0.1241379311) equal to 0.207355812 and -0.207355812.Subproblem 1
x + -0.1241379311 = 0.207355812 Simplifying x + -0.1241379311 = 0.207355812 Reorder the terms: -0.1241379311 + x = 0.207355812 Solving -0.1241379311 + x = 0.207355812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1241379311' to each side of the equation. -0.1241379311 + 0.1241379311 + x = 0.207355812 + 0.1241379311 Combine like terms: -0.1241379311 + 0.1241379311 = 0.0000000000 0.0000000000 + x = 0.207355812 + 0.1241379311 x = 0.207355812 + 0.1241379311 Combine like terms: 0.207355812 + 0.1241379311 = 0.3314937431 x = 0.3314937431 Simplifying x = 0.3314937431Subproblem 2
x + -0.1241379311 = -0.207355812 Simplifying x + -0.1241379311 = -0.207355812 Reorder the terms: -0.1241379311 + x = -0.207355812 Solving -0.1241379311 + x = -0.207355812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1241379311' to each side of the equation. -0.1241379311 + 0.1241379311 + x = -0.207355812 + 0.1241379311 Combine like terms: -0.1241379311 + 0.1241379311 = 0.0000000000 0.0000000000 + x = -0.207355812 + 0.1241379311 x = -0.207355812 + 0.1241379311 Combine like terms: -0.207355812 + 0.1241379311 = -0.0832178809 x = -0.0832178809 Simplifying x = -0.0832178809Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3314937431, -0.0832178809}
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