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Simplifying -5x2 + -19x + 40 = 0 Reorder the terms: 40 + -19x + -5x2 = 0 Solving 40 + -19x + -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'. -8 + 3.8x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 3.8x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 3.8x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3.8x + x2 = 0 + 8 3.8x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3.8x + x2 = 8 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 8 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 8 + 3.61 Combine like terms: 8 + 3.61 = 11.61 3.61 + 3.8x + x2 = 11.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 11.61 Calculate the square root of the right side: 3.407345007 Break this problem into two subproblems by setting (x + 1.9) equal to 3.407345007 and -3.407345007.Subproblem 1
x + 1.9 = 3.407345007 Simplifying x + 1.9 = 3.407345007 Reorder the terms: 1.9 + x = 3.407345007 Solving 1.9 + x = 3.407345007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 3.407345007 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 3.407345007 + -1.9 x = 3.407345007 + -1.9 Combine like terms: 3.407345007 + -1.9 = 1.507345007 x = 1.507345007 Simplifying x = 1.507345007Subproblem 2
x + 1.9 = -3.407345007 Simplifying x + 1.9 = -3.407345007 Reorder the terms: 1.9 + x = -3.407345007 Solving 1.9 + x = -3.407345007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -3.407345007 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -3.407345007 + -1.9 x = -3.407345007 + -1.9 Combine like terms: -3.407345007 + -1.9 = -5.307345007 x = -5.307345007 Simplifying x = -5.307345007Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.507345007, -5.307345007}
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