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Simplifying 5x2 + 15x + 9 = 0 Reorder the terms: 9 + 15x + 5x2 = 0 Solving 9 + 15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + 3x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 3x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 3x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 3x + x2 = 0 + -1.8 3x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 3x + x2 = -1.8 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.8 + 2.25 Combine like terms: -1.8 + 2.25 = 0.45 2.25 + 3x + x2 = 0.45 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + 1.5) equal to 0.670820393 and -0.670820393.Subproblem 1
x + 1.5 = 0.670820393 Simplifying x + 1.5 = 0.670820393 Reorder the terms: 1.5 + x = 0.670820393 Solving 1.5 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.670820393 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.670820393 + -1.5 x = 0.670820393 + -1.5 Combine like terms: 0.670820393 + -1.5 = -0.829179607 x = -0.829179607 Simplifying x = -0.829179607Subproblem 2
x + 1.5 = -0.670820393 Simplifying x + 1.5 = -0.670820393 Reorder the terms: 1.5 + x = -0.670820393 Solving 1.5 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.670820393 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.670820393 + -1.5 x = -0.670820393 + -1.5 Combine like terms: -0.670820393 + -1.5 = -2.170820393 x = -2.170820393 Simplifying x = -2.170820393Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.829179607, -2.170820393}
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