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Simplifying -2x2 + -18x = -1 Reorder the terms: -18x + -2x2 = -1 Solving -18x + -2x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -18x + -2x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -18x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 9x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 9x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 9x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 9x + x2 = 0 + 0.5 9x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 9x + x2 = 0.5 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 = 0.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 0.5 + 20.25 Combine like terms: 0.5 + 20.25 = 20.75 20.25 + 9x + x2 = 20.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 20.75 Calculate the square root of the right side: 4.55521679 Break this problem into two subproblems by setting (x + 4.5) equal to 4.55521679 and -4.55521679.Subproblem 1
x + 4.5 = 4.55521679 Simplifying x + 4.5 = 4.55521679 Reorder the terms: 4.5 + x = 4.55521679 Solving 4.5 + x = 4.55521679 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 = 4.55521679 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.55521679 + -4.5 x = 4.55521679 + -4.5 Combine like terms: 4.55521679 + -4.5 = 0.05521679 x = 0.05521679 Simplifying x = 0.05521679Subproblem 2
x + 4.5 = -4.55521679 Simplifying x + 4.5 = -4.55521679 Reorder the terms: 4.5 + x = -4.55521679 Solving 4.5 + x = -4.55521679 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 = -4.55521679 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.55521679 + -4.5 x = -4.55521679 + -4.5 Combine like terms: -4.55521679 + -4.5 = -9.05521679 x = -9.05521679 Simplifying x = -9.05521679Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.05521679, -9.05521679}
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