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Simplifying 13x2 + -104x + 178 = 26 Reorder the terms: 178 + -104x + 13x2 = 26 Solving 178 + -104x + 13x2 = 26 Solving for variable 'x'. Reorder the terms: 178 + -26 + -104x + 13x2 = 26 + -26 Combine like terms: 178 + -26 = 152 152 + -104x + 13x2 = 26 + -26 Combine like terms: 26 + -26 = 0 152 + -104x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 11.69230769 + -8x + x2 = 0 Move the constant term to the right: Add '-11.69230769' to each side of the equation. 11.69230769 + -8x + -11.69230769 + x2 = 0 + -11.69230769 Reorder the terms: 11.69230769 + -11.69230769 + -8x + x2 = 0 + -11.69230769 Combine like terms: 11.69230769 + -11.69230769 = 0.00000000 0.00000000 + -8x + x2 = 0 + -11.69230769 -8x + x2 = 0 + -11.69230769 Combine like terms: 0 + -11.69230769 = -11.69230769 -8x + x2 = -11.69230769 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -11.69230769 + 16 Reorder the terms: 16 + -8x + x2 = -11.69230769 + 16 Combine like terms: -11.69230769 + 16 = 4.30769231 16 + -8x + x2 = 4.30769231 Factor a perfect square on the left side: (x + -4)(x + -4) = 4.30769231 Calculate the square root of the right side: 2.075498087 Break this problem into two subproblems by setting (x + -4) equal to 2.075498087 and -2.075498087.Subproblem 1
x + -4 = 2.075498087 Simplifying x + -4 = 2.075498087 Reorder the terms: -4 + x = 2.075498087 Solving -4 + x = 2.075498087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.075498087 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.075498087 + 4 x = 2.075498087 + 4 Combine like terms: 2.075498087 + 4 = 6.075498087 x = 6.075498087 Simplifying x = 6.075498087Subproblem 2
x + -4 = -2.075498087 Simplifying x + -4 = -2.075498087 Reorder the terms: -4 + x = -2.075498087 Solving -4 + x = -2.075498087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.075498087 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.075498087 + 4 x = -2.075498087 + 4 Combine like terms: -2.075498087 + 4 = 1.924501913 x = 1.924501913 Simplifying x = 1.924501913Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.075498087, 1.924501913}
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