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Simplifying 2x2 + -18x + -2891 = 0 Reorder the terms: -2891 + -18x + 2x2 = 0 Solving -2891 + -18x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1445.5 + -9x + x2 = 0 Move the constant term to the right: Add '1445.5' to each side of the equation. -1445.5 + -9x + 1445.5 + x2 = 0 + 1445.5 Reorder the terms: -1445.5 + 1445.5 + -9x + x2 = 0 + 1445.5 Combine like terms: -1445.5 + 1445.5 = 0.0 0.0 + -9x + x2 = 0 + 1445.5 -9x + x2 = 0 + 1445.5 Combine like terms: 0 + 1445.5 = 1445.5 -9x + x2 = 1445.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 1445.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 1445.5 + 20.25 Combine like terms: 1445.5 + 20.25 = 1465.75 20.25 + -9x + x2 = 1465.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 1465.75 Calculate the square root of the right side: 38.285114601 Break this problem into two subproblems by setting (x + -4.5) equal to 38.285114601 and -38.285114601.Subproblem 1
x + -4.5 = 38.285114601 Simplifying x + -4.5 = 38.285114601 Reorder the terms: -4.5 + x = 38.285114601 Solving -4.5 + x = 38.285114601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 38.285114601 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 38.285114601 + 4.5 x = 38.285114601 + 4.5 Combine like terms: 38.285114601 + 4.5 = 42.785114601 x = 42.785114601 Simplifying x = 42.785114601Subproblem 2
x + -4.5 = -38.285114601 Simplifying x + -4.5 = -38.285114601 Reorder the terms: -4.5 + x = -38.285114601 Solving -4.5 + x = -38.285114601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -38.285114601 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -38.285114601 + 4.5 x = -38.285114601 + 4.5 Combine like terms: -38.285114601 + 4.5 = -33.785114601 x = -33.785114601 Simplifying x = -33.785114601Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.785114601, -33.785114601}
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