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Simplifying 5x2 + 16x + 9 = 0 Reorder the terms: 9 + 16x + 5x2 = 0 Solving 9 + 16x + 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 + 3.2x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + 3.2x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + 3.2x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 3.2x + x2 = 0 + -1.8 3.2x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 3.2x + x2 = -1.8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -1.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -1.8 + 2.56 Combine like terms: -1.8 + 2.56 = 0.76 2.56 + 3.2x + x2 = 0.76 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + 1.6) equal to 0.871779789 and -0.871779789.Subproblem 1
x + 1.6 = 0.871779789 Simplifying x + 1.6 = 0.871779789 Reorder the terms: 1.6 + x = 0.871779789 Solving 1.6 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 0.871779789 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 0.871779789 + -1.6 x = 0.871779789 + -1.6 Combine like terms: 0.871779789 + -1.6 = -0.728220211 x = -0.728220211 Simplifying x = -0.728220211Subproblem 2
x + 1.6 = -0.871779789 Simplifying x + 1.6 = -0.871779789 Reorder the terms: 1.6 + x = -0.871779789 Solving 1.6 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -0.871779789 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -0.871779789 + -1.6 x = -0.871779789 + -1.6 Combine like terms: -0.871779789 + -1.6 = -2.471779789 x = -2.471779789 Simplifying x = -2.471779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.728220211, -2.471779789}
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