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Simplifying 2x2 + 6x + -19 = 0 Reorder the terms: -19 + 6x + 2x2 = 0 Solving -19 + 6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 3x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 3x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 3x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 3x + x2 = 0 + 9.5 3x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 3x + x2 = 9.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 9.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 9.5 + 2.25 Combine like terms: 9.5 + 2.25 = 11.75 2.25 + 3x + x2 = 11.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + 1.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + 1.5 = 3.4278273 Simplifying x + 1.5 = 3.4278273 Reorder the terms: 1.5 + x = 3.4278273 Solving 1.5 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.4278273 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.4278273 + -1.5 x = 3.4278273 + -1.5 Combine like terms: 3.4278273 + -1.5 = 1.9278273 x = 1.9278273 Simplifying x = 1.9278273Subproblem 2
x + 1.5 = -3.4278273 Simplifying x + 1.5 = -3.4278273 Reorder the terms: 1.5 + x = -3.4278273 Solving 1.5 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.4278273 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.4278273 + -1.5 x = -3.4278273 + -1.5 Combine like terms: -3.4278273 + -1.5 = -4.9278273 x = -4.9278273 Simplifying x = -4.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9278273, -4.9278273}
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