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Simplifying 2x2 + -19x + -6 = 0 Reorder the terms: -6 + -19x + 2x2 = 0 Solving -6 + -19x + 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'. -3 + -9.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -9.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -9.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9.5x + x2 = 0 + 3 -9.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9.5x + x2 = 3 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 3 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 3 + 22.5625 Combine like terms: 3 + 22.5625 = 25.5625 22.5625 + -9.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -4.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -4.75 = 5.055937104 Simplifying x + -4.75 = 5.055937104 Reorder the terms: -4.75 + x = 5.055937104 Solving -4.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.055937104 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.055937104 + 4.75 x = 5.055937104 + 4.75 Combine like terms: 5.055937104 + 4.75 = 9.805937104 x = 9.805937104 Simplifying x = 9.805937104Subproblem 2
x + -4.75 = -5.055937104 Simplifying x + -4.75 = -5.055937104 Reorder the terms: -4.75 + x = -5.055937104 Solving -4.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.055937104 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.055937104 + 4.75 x = -5.055937104 + 4.75 Combine like terms: -5.055937104 + 4.75 = -0.305937104 x = -0.305937104 Simplifying x = -0.305937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.805937104, -0.305937104}
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