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Simplifying x2 + -2x + 1 = 80 Reorder the terms: 1 + -2x + x2 = 80 Solving 1 + -2x + x2 = 80 Solving for variable 'x'. Reorder the terms: 1 + -80 + -2x + x2 = 80 + -80 Combine like terms: 1 + -80 = -79 -79 + -2x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -79 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -2x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + -2x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -2x + x2 = 0 + 79 -2x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 -2x + x2 = 79 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 79 + 1 Reorder the terms: 1 + -2x + x2 = 79 + 1 Combine like terms: 79 + 1 = 80 1 + -2x + x2 = 80 Factor a perfect square on the left side: (x + -1)(x + -1) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -1) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -1 = 8.94427191 Simplifying x + -1 = 8.94427191 Reorder the terms: -1 + x = 8.94427191 Solving -1 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.94427191 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.94427191 + 1 x = 8.94427191 + 1 Combine like terms: 8.94427191 + 1 = 9.94427191 x = 9.94427191 Simplifying x = 9.94427191Subproblem 2
x + -1 = -8.94427191 Simplifying x + -1 = -8.94427191 Reorder the terms: -1 + x = -8.94427191 Solving -1 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.94427191 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.94427191 + 1 x = -8.94427191 + 1 Combine like terms: -8.94427191 + 1 = -7.94427191 x = -7.94427191 Simplifying x = -7.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.94427191, -7.94427191}
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