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Simplifying 5x2 + 20x + 19 = 0 Reorder the terms: 19 + 20x + 5x2 = 0 Solving 19 + 20x + 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'. 3.8 + 4x + x2 = 0 Move the constant term to the right: Add '-3.8' to each side of the equation. 3.8 + 4x + -3.8 + x2 = 0 + -3.8 Reorder the terms: 3.8 + -3.8 + 4x + x2 = 0 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + 4x + x2 = 0 + -3.8 4x + x2 = 0 + -3.8 Combine like terms: 0 + -3.8 = -3.8 4x + x2 = -3.8 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.8 + 4 Reorder the terms: 4 + 4x + x2 = -3.8 + 4 Combine like terms: -3.8 + 4 = 0.2 4 + 4x + x2 = 0.2 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + 2) equal to 0.447213596 and -0.447213596.Subproblem 1
x + 2 = 0.447213596 Simplifying x + 2 = 0.447213596 Reorder the terms: 2 + x = 0.447213596 Solving 2 + x = 0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.447213596 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.447213596 + -2 x = 0.447213596 + -2 Combine like terms: 0.447213596 + -2 = -1.552786404 x = -1.552786404 Simplifying x = -1.552786404Subproblem 2
x + 2 = -0.447213596 Simplifying x + 2 = -0.447213596 Reorder the terms: 2 + x = -0.447213596 Solving 2 + x = -0.447213596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.447213596 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.447213596 + -2 x = -0.447213596 + -2 Combine like terms: -0.447213596 + -2 = -2.447213596 x = -2.447213596 Simplifying x = -2.447213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.552786404, -2.447213596}
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