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Simplifying 0 = x2 + -42x + 371 Reorder the terms: 0 = 371 + -42x + x2 Solving 0 = 371 + -42x + x2 Solving for variable 'x'. Combine like terms: 0 + -371 = -371 -371 + 42x + -1x2 = 371 + -42x + x2 + -371 + 42x + -1x2 Reorder the terms: -371 + 42x + -1x2 = 371 + -371 + -42x + 42x + x2 + -1x2 Combine like terms: 371 + -371 = 0 -371 + 42x + -1x2 = 0 + -42x + 42x + x2 + -1x2 -371 + 42x + -1x2 = -42x + 42x + x2 + -1x2 Combine like terms: -42x + 42x = 0 -371 + 42x + -1x2 = 0 + x2 + -1x2 -371 + 42x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -371 + 42x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 371 + -42x + x2 = 0 Move the constant term to the right: Add '-371' to each side of the equation. 371 + -42x + -371 + x2 = 0 + -371 Reorder the terms: 371 + -371 + -42x + x2 = 0 + -371 Combine like terms: 371 + -371 = 0 0 + -42x + x2 = 0 + -371 -42x + x2 = 0 + -371 Combine like terms: 0 + -371 = -371 -42x + x2 = -371 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -371 + 441 Reorder the terms: 441 + -42x + x2 = -371 + 441 Combine like terms: -371 + 441 = 70 441 + -42x + x2 = 70 Factor a perfect square on the left side: (x + -21)(x + -21) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -21) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -21 = 8.366600265 Simplifying x + -21 = 8.366600265 Reorder the terms: -21 + x = 8.366600265 Solving -21 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 8.366600265 + 21 Combine like terms: -21 + 21 = 0 0 + x = 8.366600265 + 21 x = 8.366600265 + 21 Combine like terms: 8.366600265 + 21 = 29.366600265 x = 29.366600265 Simplifying x = 29.366600265Subproblem 2
x + -21 = -8.366600265 Simplifying x + -21 = -8.366600265 Reorder the terms: -21 + x = -8.366600265 Solving -21 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -8.366600265 + 21 Combine like terms: -21 + 21 = 0 0 + x = -8.366600265 + 21 x = -8.366600265 + 21 Combine like terms: -8.366600265 + 21 = 12.633399735 x = 12.633399735 Simplifying x = 12.633399735Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.366600265, 12.633399735}
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