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Simplifying x2 + -2x + -84 = 0 Reorder the terms: -84 + -2x + x2 = 0 Solving -84 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -2x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -2x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -2x + x2 = 0 + 84 -2x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -2x + x2 = 84 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 = 84 + 1 Reorder the terms: 1 + -2x + x2 = 84 + 1 Combine like terms: 84 + 1 = 85 1 + -2x + x2 = 85 Factor a perfect square on the left side: (x + -1)(x + -1) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -1) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -1 = 9.219544457 Simplifying x + -1 = 9.219544457 Reorder the terms: -1 + x = 9.219544457 Solving -1 + x = 9.219544457 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 = 9.219544457 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.219544457 + 1 x = 9.219544457 + 1 Combine like terms: 9.219544457 + 1 = 10.219544457 x = 10.219544457 Simplifying x = 10.219544457Subproblem 2
x + -1 = -9.219544457 Simplifying x + -1 = -9.219544457 Reorder the terms: -1 + x = -9.219544457 Solving -1 + x = -9.219544457 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 = -9.219544457 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.219544457 + 1 x = -9.219544457 + 1 Combine like terms: -9.219544457 + 1 = -8.219544457 x = -8.219544457 Simplifying x = -8.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.219544457, -8.219544457}
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