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Simplifying 2x2 + -19x + -5 = 0 Reorder the terms: -5 + -19x + 2x2 = 0 Solving -5 + -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'. -2.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -9.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -9.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -9.5x + x2 = 0 + 2.5 -9.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -9.5x + x2 = 2.5 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 = 2.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 2.5 + 22.5625 Combine like terms: 2.5 + 22.5625 = 25.0625 22.5625 + -9.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + -4.75) equal to 5.006246099 and -5.006246099.Subproblem 1
x + -4.75 = 5.006246099 Simplifying x + -4.75 = 5.006246099 Reorder the terms: -4.75 + x = 5.006246099 Solving -4.75 + x = 5.006246099 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 = 5.006246099 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.006246099 + 4.75 x = 5.006246099 + 4.75 Combine like terms: 5.006246099 + 4.75 = 9.756246099 x = 9.756246099 Simplifying x = 9.756246099Subproblem 2
x + -4.75 = -5.006246099 Simplifying x + -4.75 = -5.006246099 Reorder the terms: -4.75 + x = -5.006246099 Solving -4.75 + x = -5.006246099 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 = -5.006246099 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.006246099 + 4.75 x = -5.006246099 + 4.75 Combine like terms: -5.006246099 + 4.75 = -0.256246099 x = -0.256246099 Simplifying x = -0.256246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.756246099, -0.256246099}
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