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Simplifying 5x2 + 38x + 16 = 0 Reorder the terms: 16 + 38x + 5x2 = 0 Solving 16 + 38x + 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'. 3.2 + 7.6x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + 7.6x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + 7.6x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + 7.6x + x2 = 0 + -3.2 7.6x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 7.6x + x2 = -3.2 The x term is 7.6x. Take half its coefficient (3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. 7.6x + 14.44 + x2 = -3.2 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = -3.2 + 14.44 Combine like terms: -3.2 + 14.44 = 11.24 14.44 + 7.6x + x2 = 11.24 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 11.24 Calculate the square root of the right side: 3.352610923 Break this problem into two subproblems by setting (x + 3.8) equal to 3.352610923 and -3.352610923.Subproblem 1
x + 3.8 = 3.352610923 Simplifying x + 3.8 = 3.352610923 Reorder the terms: 3.8 + x = 3.352610923 Solving 3.8 + x = 3.352610923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = 3.352610923 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 3.352610923 + -3.8 x = 3.352610923 + -3.8 Combine like terms: 3.352610923 + -3.8 = -0.447389077 x = -0.447389077 Simplifying x = -0.447389077Subproblem 2
x + 3.8 = -3.352610923 Simplifying x + 3.8 = -3.352610923 Reorder the terms: 3.8 + x = -3.352610923 Solving 3.8 + x = -3.352610923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = -3.352610923 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -3.352610923 + -3.8 x = -3.352610923 + -3.8 Combine like terms: -3.352610923 + -3.8 = -7.152610923 x = -7.152610923 Simplifying x = -7.152610923Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.447389077, -7.152610923}
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