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Simplifying 26x2 + -260x + 556 = 0 Reorder the terms: 556 + -260x + 26x2 = 0 Solving 556 + -260x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(278 + -130x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(278 + -130x + 13x2)' equal to zero and attempt to solve: Simplifying 278 + -130x + 13x2 = 0 Solving 278 + -130x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 21.38461538 + -10x + x2 = 0 Move the constant term to the right: Add '-21.38461538' to each side of the equation. 21.38461538 + -10x + -21.38461538 + x2 = 0 + -21.38461538 Reorder the terms: 21.38461538 + -21.38461538 + -10x + x2 = 0 + -21.38461538 Combine like terms: 21.38461538 + -21.38461538 = 0.00000000 0.00000000 + -10x + x2 = 0 + -21.38461538 -10x + x2 = 0 + -21.38461538 Combine like terms: 0 + -21.38461538 = -21.38461538 -10x + x2 = -21.38461538 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -21.38461538 + 25 Reorder the terms: 25 + -10x + x2 = -21.38461538 + 25 Combine like terms: -21.38461538 + 25 = 3.61538462 25 + -10x + x2 = 3.61538462 Factor a perfect square on the left side: (x + -5)(x + -5) = 3.61538462 Calculate the square root of the right side: 1.901416477 Break this problem into two subproblems by setting (x + -5) equal to 1.901416477 and -1.901416477.Subproblem 1
x + -5 = 1.901416477 Simplifying x + -5 = 1.901416477 Reorder the terms: -5 + x = 1.901416477 Solving -5 + x = 1.901416477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 1.901416477 + 5 Combine like terms: -5 + 5 = 0 0 + x = 1.901416477 + 5 x = 1.901416477 + 5 Combine like terms: 1.901416477 + 5 = 6.901416477 x = 6.901416477 Simplifying x = 6.901416477Subproblem 2
x + -5 = -1.901416477 Simplifying x + -5 = -1.901416477 Reorder the terms: -5 + x = -1.901416477 Solving -5 + x = -1.901416477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -1.901416477 + 5 Combine like terms: -5 + 5 = 0 0 + x = -1.901416477 + 5 x = -1.901416477 + 5 Combine like terms: -1.901416477 + 5 = 3.098583523 x = 3.098583523 Simplifying x = 3.098583523Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.901416477, 3.098583523}Solution
x = {6.901416477, 3.098583523}
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