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Simplifying x2 + -1x + -1991 = 0 Reorder the terms: -1991 + -1x + x2 = 0 Solving -1991 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1991' to each side of the equation. -1991 + -1x + 1991 + x2 = 0 + 1991 Reorder the terms: -1991 + 1991 + -1x + x2 = 0 + 1991 Combine like terms: -1991 + 1991 = 0 0 + -1x + x2 = 0 + 1991 -1x + x2 = 0 + 1991 Combine like terms: 0 + 1991 = 1991 -1x + x2 = 1991 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1991 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1991 + 0.25 Combine like terms: 1991 + 0.25 = 1991.25 0.25 + -1x + x2 = 1991.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1991.25 Calculate the square root of the right side: 44.623424342 Break this problem into two subproblems by setting (x + -0.5) equal to 44.623424342 and -44.623424342.Subproblem 1
x + -0.5 = 44.623424342 Simplifying x + -0.5 = 44.623424342 Reorder the terms: -0.5 + x = 44.623424342 Solving -0.5 + x = 44.623424342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 44.623424342 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 44.623424342 + 0.5 x = 44.623424342 + 0.5 Combine like terms: 44.623424342 + 0.5 = 45.123424342 x = 45.123424342 Simplifying x = 45.123424342Subproblem 2
x + -0.5 = -44.623424342 Simplifying x + -0.5 = -44.623424342 Reorder the terms: -0.5 + x = -44.623424342 Solving -0.5 + x = -44.623424342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -44.623424342 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -44.623424342 + 0.5 x = -44.623424342 + 0.5 Combine like terms: -44.623424342 + 0.5 = -44.123424342 x = -44.123424342 Simplifying x = -44.123424342Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.123424342, -44.123424342}
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