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Simplifying 2x2 + 18x = 5 Reorder the terms: 18x + 2x2 = 5 Solving 18x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 18x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 9x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 9x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 9x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 9x + x2 = 0 + 2.5 9x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 9x + x2 = 2.5 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 = 2.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 2.5 + 20.25 Combine like terms: 2.5 + 20.25 = 22.75 20.25 + 9x + x2 = 22.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + 4.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + 4.5 = 4.769696007 Simplifying x + 4.5 = 4.769696007 Reorder the terms: 4.5 + x = 4.769696007 Solving 4.5 + x = 4.769696007 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 = 4.769696007 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.769696007 + -4.5 x = 4.769696007 + -4.5 Combine like terms: 4.769696007 + -4.5 = 0.269696007 x = 0.269696007 Simplifying x = 0.269696007Subproblem 2
x + 4.5 = -4.769696007 Simplifying x + 4.5 = -4.769696007 Reorder the terms: 4.5 + x = -4.769696007 Solving 4.5 + x = -4.769696007 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 = -4.769696007 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.769696007 + -4.5 x = -4.769696007 + -4.5 Combine like terms: -4.769696007 + -4.5 = -9.269696007 x = -9.269696007 Simplifying x = -9.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.269696007, -9.269696007}
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