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Simplifying 2x2 + 2 = 13x Reorder the terms: 2 + 2x2 = 13x Solving 2 + 2x2 = 13x Solving for variable 'x'. Reorder the terms: 2 + -13x + 2x2 = 13x + -13x Combine like terms: 13x + -13x = 0 2 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -6.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -6.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6.5x + x2 = 0 + -1 -6.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6.5x + x2 = -1 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 = -1 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -1 + 10.5625 Combine like terms: -1 + 10.5625 = 9.5625 10.5625 + -6.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + -3.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + -3.25 = 3.092329219 Simplifying x + -3.25 = 3.092329219 Reorder the terms: -3.25 + x = 3.092329219 Solving -3.25 + x = 3.092329219 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 = 3.092329219 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.092329219 + 3.25 x = 3.092329219 + 3.25 Combine like terms: 3.092329219 + 3.25 = 6.342329219 x = 6.342329219 Simplifying x = 6.342329219Subproblem 2
x + -3.25 = -3.092329219 Simplifying x + -3.25 = -3.092329219 Reorder the terms: -3.25 + x = -3.092329219 Solving -3.25 + x = -3.092329219 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 = -3.092329219 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.092329219 + 3.25 x = -3.092329219 + 3.25 Combine like terms: -3.092329219 + 3.25 = 0.157670781 x = 0.157670781 Simplifying x = 0.157670781Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.342329219, 0.157670781}
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