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Simplifying 2x2 + -31x + 72 = 0 Reorder the terms: 72 + -31x + 2x2 = 0 Solving 72 + -31x + 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'. 36 + -15.5x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -15.5x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -15.5x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -15.5x + x2 = 0 + -36 -15.5x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -15.5x + x2 = -36 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = -36 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = -36 + 60.0625 Combine like terms: -36 + 60.0625 = 24.0625 60.0625 + -15.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + -7.75) equal to 4.905354218 and -4.905354218.Subproblem 1
x + -7.75 = 4.905354218 Simplifying x + -7.75 = 4.905354218 Reorder the terms: -7.75 + x = 4.905354218 Solving -7.75 + x = 4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 4.905354218 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 4.905354218 + 7.75 x = 4.905354218 + 7.75 Combine like terms: 4.905354218 + 7.75 = 12.655354218 x = 12.655354218 Simplifying x = 12.655354218Subproblem 2
x + -7.75 = -4.905354218 Simplifying x + -7.75 = -4.905354218 Reorder the terms: -7.75 + x = -4.905354218 Solving -7.75 + x = -4.905354218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -4.905354218 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -4.905354218 + 7.75 x = -4.905354218 + 7.75 Combine like terms: -4.905354218 + 7.75 = 2.844645782 x = 2.844645782 Simplifying x = 2.844645782Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.655354218, 2.844645782}
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