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Simplifying 2x2 + -38x + -325 = 0 Reorder the terms: -325 + -38x + 2x2 = 0 Solving -325 + -38x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -162.5 + -19x + x2 = 0 Move the constant term to the right: Add '162.5' to each side of the equation. -162.5 + -19x + 162.5 + x2 = 0 + 162.5 Reorder the terms: -162.5 + 162.5 + -19x + x2 = 0 + 162.5 Combine like terms: -162.5 + 162.5 = 0.0 0.0 + -19x + x2 = 0 + 162.5 -19x + x2 = 0 + 162.5 Combine like terms: 0 + 162.5 = 162.5 -19x + x2 = 162.5 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 162.5 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 162.5 + 90.25 Combine like terms: 162.5 + 90.25 = 252.75 90.25 + -19x + x2 = 252.75 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 252.75 Calculate the square root of the right side: 15.898113096 Break this problem into two subproblems by setting (x + -9.5) equal to 15.898113096 and -15.898113096.Subproblem 1
x + -9.5 = 15.898113096 Simplifying x + -9.5 = 15.898113096 Reorder the terms: -9.5 + x = 15.898113096 Solving -9.5 + x = 15.898113096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 15.898113096 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 15.898113096 + 9.5 x = 15.898113096 + 9.5 Combine like terms: 15.898113096 + 9.5 = 25.398113096 x = 25.398113096 Simplifying x = 25.398113096Subproblem 2
x + -9.5 = -15.898113096 Simplifying x + -9.5 = -15.898113096 Reorder the terms: -9.5 + x = -15.898113096 Solving -9.5 + x = -15.898113096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -15.898113096 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -15.898113096 + 9.5 x = -15.898113096 + 9.5 Combine like terms: -15.898113096 + 9.5 = -6.398113096 x = -6.398113096 Simplifying x = -6.398113096Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.398113096, -6.398113096}
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