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Simplifying 1x2 + 9x + 19 = 0 Reorder the terms: 19 + 9x + 1x2 = 0 Solving 19 + 9x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 9x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 9x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 9x + x2 = 0 + -19 9x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 9x + x2 = -19 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 = -19 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -19 + 20.25 Combine like terms: -19 + 20.25 = 1.25 20.25 + 9x + x2 = 1.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 4.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 4.5 = 1.118033989 Simplifying x + 4.5 = 1.118033989 Reorder the terms: 4.5 + x = 1.118033989 Solving 4.5 + x = 1.118033989 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 = 1.118033989 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 1.118033989 + -4.5 x = 1.118033989 + -4.5 Combine like terms: 1.118033989 + -4.5 = -3.381966011 x = -3.381966011 Simplifying x = -3.381966011Subproblem 2
x + 4.5 = -1.118033989 Simplifying x + 4.5 = -1.118033989 Reorder the terms: 4.5 + x = -1.118033989 Solving 4.5 + x = -1.118033989 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 = -1.118033989 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -1.118033989 + -4.5 x = -1.118033989 + -4.5 Combine like terms: -1.118033989 + -4.5 = -5.618033989 x = -5.618033989 Simplifying x = -5.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.381966011, -5.618033989}
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