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Simplifying 2x2 + 18x + 5 = 0 Reorder the terms: 5 + 18x + 2x2 = 0 Solving 5 + 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'. 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 = 17.75 20.25 + 9x + x2 = 17.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + 4.5) equal to 4.213074887 and -4.213074887.Subproblem 1
x + 4.5 = 4.213074887 Simplifying x + 4.5 = 4.213074887 Reorder the terms: 4.5 + x = 4.213074887 Solving 4.5 + x = 4.213074887 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 = 4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.213074887 + -4.5 x = 4.213074887 + -4.5 Combine like terms: 4.213074887 + -4.5 = -0.286925113 x = -0.286925113 Simplifying x = -0.286925113Subproblem 2
x + 4.5 = -4.213074887 Simplifying x + 4.5 = -4.213074887 Reorder the terms: 4.5 + x = -4.213074887 Solving 4.5 + x = -4.213074887 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 = -4.213074887 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.213074887 + -4.5 x = -4.213074887 + -4.5 Combine like terms: -4.213074887 + -4.5 = -8.713074887 x = -8.713074887 Simplifying x = -8.713074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.286925113, -8.713074887}
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