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Simplifying x2 + 19x + -4 = 0 Reorder the terms: -4 + 19x + x2 = 0 Solving -4 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 19x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 19x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 19x + x2 = 0 + 4 19x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 19x + x2 = 4 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 4 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 4 + 90.25 Combine like terms: 4 + 90.25 = 94.25 90.25 + 19x + x2 = 94.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 9.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 9.5 = 9.708243919 Simplifying x + 9.5 = 9.708243919 Reorder the terms: 9.5 + x = 9.708243919 Solving 9.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.708243919 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.708243919 + -9.5 x = 9.708243919 + -9.5 Combine like terms: 9.708243919 + -9.5 = 0.208243919 x = 0.208243919 Simplifying x = 0.208243919Subproblem 2
x + 9.5 = -9.708243919 Simplifying x + 9.5 = -9.708243919 Reorder the terms: 9.5 + x = -9.708243919 Solving 9.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.708243919 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.708243919 + -9.5 x = -9.708243919 + -9.5 Combine like terms: -9.708243919 + -9.5 = -19.208243919 x = -19.208243919 Simplifying x = -19.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.208243919, -19.208243919}
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