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Simplifying 5x2 + 30x + -19 = 0 Reorder the terms: -19 + 30x + 5x2 = 0 Solving -19 + 30x + 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 + 6x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 6x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 6x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 6x + x2 = 0 + 3.8 6x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 6x + x2 = 3.8 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.8 + 9 Reorder the terms: 9 + 6x + x2 = 3.8 + 9 Combine like terms: 3.8 + 9 = 12.8 9 + 6x + x2 = 12.8 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.8 Calculate the square root of the right side: 3.577708764 Break this problem into two subproblems by setting (x + 3) equal to 3.577708764 and -3.577708764.Subproblem 1
x + 3 = 3.577708764 Simplifying x + 3 = 3.577708764 Reorder the terms: 3 + x = 3.577708764 Solving 3 + x = 3.577708764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.577708764 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.577708764 + -3 x = 3.577708764 + -3 Combine like terms: 3.577708764 + -3 = 0.577708764 x = 0.577708764 Simplifying x = 0.577708764Subproblem 2
x + 3 = -3.577708764 Simplifying x + 3 = -3.577708764 Reorder the terms: 3 + x = -3.577708764 Solving 3 + x = -3.577708764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.577708764 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.577708764 + -3 x = -3.577708764 + -3 Combine like terms: -3.577708764 + -3 = -6.577708764 x = -6.577708764 Simplifying x = -6.577708764Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.577708764, -6.577708764}
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