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Simplifying 0 = x2 + -31x + 74 Reorder the terms: 0 = 74 + -31x + x2 Solving 0 = 74 + -31x + x2 Solving for variable 'x'. Combine like terms: 0 + -74 = -74 -74 + 31x + -1x2 = 74 + -31x + x2 + -74 + 31x + -1x2 Reorder the terms: -74 + 31x + -1x2 = 74 + -74 + -31x + 31x + x2 + -1x2 Combine like terms: 74 + -74 = 0 -74 + 31x + -1x2 = 0 + -31x + 31x + x2 + -1x2 -74 + 31x + -1x2 = -31x + 31x + x2 + -1x2 Combine like terms: -31x + 31x = 0 -74 + 31x + -1x2 = 0 + x2 + -1x2 -74 + 31x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -74 + 31x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 74 + -31x + x2 = 0 Move the constant term to the right: Add '-74' to each side of the equation. 74 + -31x + -74 + x2 = 0 + -74 Reorder the terms: 74 + -74 + -31x + x2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -31x + x2 = 0 + -74 -31x + x2 = 0 + -74 Combine like terms: 0 + -74 = -74 -31x + x2 = -74 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -74 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -74 + 240.25 Combine like terms: -74 + 240.25 = 166.25 240.25 + -31x + x2 = 166.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 166.25 Calculate the square root of the right side: 12.893796958 Break this problem into two subproblems by setting (x + -15.5) equal to 12.893796958 and -12.893796958.Subproblem 1
x + -15.5 = 12.893796958 Simplifying x + -15.5 = 12.893796958 Reorder the terms: -15.5 + x = 12.893796958 Solving -15.5 + x = 12.893796958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 12.893796958 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 12.893796958 + 15.5 x = 12.893796958 + 15.5 Combine like terms: 12.893796958 + 15.5 = 28.393796958 x = 28.393796958 Simplifying x = 28.393796958Subproblem 2
x + -15.5 = -12.893796958 Simplifying x + -15.5 = -12.893796958 Reorder the terms: -15.5 + x = -12.893796958 Solving -15.5 + x = -12.893796958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -12.893796958 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -12.893796958 + 15.5 x = -12.893796958 + 15.5 Combine like terms: -12.893796958 + 15.5 = 2.606203042 x = 2.606203042 Simplifying x = 2.606203042Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.393796958, 2.606203042}
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