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Simplifying 2x2 + -13x + -490 = 0 Reorder the terms: -490 + -13x + 2x2 = 0 Solving -490 + -13x + 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'. -245 + -6.5x + x2 = 0 Move the constant term to the right: Add '245' to each side of the equation. -245 + -6.5x + 245 + x2 = 0 + 245 Reorder the terms: -245 + 245 + -6.5x + x2 = 0 + 245 Combine like terms: -245 + 245 = 0 0 + -6.5x + x2 = 0 + 245 -6.5x + x2 = 0 + 245 Combine like terms: 0 + 245 = 245 -6.5x + x2 = 245 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 245 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 245 + 10.5625 Combine like terms: 245 + 10.5625 = 255.5625 10.5625 + -6.5x + x2 = 255.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 255.5625 Calculate the square root of the right side: 15.986322279 Break this problem into two subproblems by setting (x + -3.25) equal to 15.986322279 and -15.986322279.Subproblem 1
x + -3.25 = 15.986322279 Simplifying x + -3.25 = 15.986322279 Reorder the terms: -3.25 + x = 15.986322279 Solving -3.25 + x = 15.986322279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 15.986322279 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 15.986322279 + 3.25 x = 15.986322279 + 3.25 Combine like terms: 15.986322279 + 3.25 = 19.236322279 x = 19.236322279 Simplifying x = 19.236322279Subproblem 2
x + -3.25 = -15.986322279 Simplifying x + -3.25 = -15.986322279 Reorder the terms: -3.25 + x = -15.986322279 Solving -3.25 + x = -15.986322279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -15.986322279 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -15.986322279 + 3.25 x = -15.986322279 + 3.25 Combine like terms: -15.986322279 + 3.25 = -12.736322279 x = -12.736322279 Simplifying x = -12.736322279Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.236322279, -12.736322279}
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