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Simplifying x2 + -71x + 416 = 0 Reorder the terms: 416 + -71x + x2 = 0 Solving 416 + -71x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-416' to each side of the equation. 416 + -71x + -416 + x2 = 0 + -416 Reorder the terms: 416 + -416 + -71x + x2 = 0 + -416 Combine like terms: 416 + -416 = 0 0 + -71x + x2 = 0 + -416 -71x + x2 = 0 + -416 Combine like terms: 0 + -416 = -416 -71x + x2 = -416 The x term is -71x. Take half its coefficient (-35.5). Square it (1260.25) and add it to both sides. Add '1260.25' to each side of the equation. -71x + 1260.25 + x2 = -416 + 1260.25 Reorder the terms: 1260.25 + -71x + x2 = -416 + 1260.25 Combine like terms: -416 + 1260.25 = 844.25 1260.25 + -71x + x2 = 844.25 Factor a perfect square on the left side: (x + -35.5)(x + -35.5) = 844.25 Calculate the square root of the right side: 29.055980452 Break this problem into two subproblems by setting (x + -35.5) equal to 29.055980452 and -29.055980452.Subproblem 1
x + -35.5 = 29.055980452 Simplifying x + -35.5 = 29.055980452 Reorder the terms: -35.5 + x = 29.055980452 Solving -35.5 + x = 29.055980452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.5' to each side of the equation. -35.5 + 35.5 + x = 29.055980452 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + x = 29.055980452 + 35.5 x = 29.055980452 + 35.5 Combine like terms: 29.055980452 + 35.5 = 64.555980452 x = 64.555980452 Simplifying x = 64.555980452Subproblem 2
x + -35.5 = -29.055980452 Simplifying x + -35.5 = -29.055980452 Reorder the terms: -35.5 + x = -29.055980452 Solving -35.5 + x = -29.055980452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.5' to each side of the equation. -35.5 + 35.5 + x = -29.055980452 + 35.5 Combine like terms: -35.5 + 35.5 = 0.0 0.0 + x = -29.055980452 + 35.5 x = -29.055980452 + 35.5 Combine like terms: -29.055980452 + 35.5 = 6.444019548 x = 6.444019548 Simplifying x = 6.444019548Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.555980452, 6.444019548}
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