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Simplifying 2x2 + -18x + -87 = 0 Reorder the terms: -87 + -18x + 2x2 = 0 Solving -87 + -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'. -43.5 + -9x + x2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + -9x + 43.5 + x2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + -9x + x2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + -9x + x2 = 0 + 43.5 -9x + x2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 -9x + x2 = 43.5 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 = 43.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 43.5 + 20.25 Combine like terms: 43.5 + 20.25 = 63.75 20.25 + -9x + x2 = 63.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 63.75 Calculate the square root of the right side: 7.984359711 Break this problem into two subproblems by setting (x + -4.5) equal to 7.984359711 and -7.984359711.Subproblem 1
x + -4.5 = 7.984359711 Simplifying x + -4.5 = 7.984359711 Reorder the terms: -4.5 + x = 7.984359711 Solving -4.5 + x = 7.984359711 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 = 7.984359711 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.984359711 + 4.5 x = 7.984359711 + 4.5 Combine like terms: 7.984359711 + 4.5 = 12.484359711 x = 12.484359711 Simplifying x = 12.484359711Subproblem 2
x + -4.5 = -7.984359711 Simplifying x + -4.5 = -7.984359711 Reorder the terms: -4.5 + x = -7.984359711 Solving -4.5 + x = -7.984359711 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 = -7.984359711 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.984359711 + 4.5 x = -7.984359711 + 4.5 Combine like terms: -7.984359711 + 4.5 = -3.484359711 x = -3.484359711 Simplifying x = -3.484359711Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.484359711, -3.484359711}
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