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Simplifying 26x2 + -8x + -9 = 0 Reorder the terms: -9 + -8x + 26x2 = 0 Solving -9 + -8x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.3461538462 + -0.3076923077x + x2 = 0 Move the constant term to the right: Add '0.3461538462' to each side of the equation. -0.3461538462 + -0.3076923077x + 0.3461538462 + x2 = 0 + 0.3461538462 Reorder the terms: -0.3461538462 + 0.3461538462 + -0.3076923077x + x2 = 0 + 0.3461538462 Combine like terms: -0.3461538462 + 0.3461538462 = 0.0000000000 0.0000000000 + -0.3076923077x + x2 = 0 + 0.3461538462 -0.3076923077x + x2 = 0 + 0.3461538462 Combine like terms: 0 + 0.3461538462 = 0.3461538462 -0.3076923077x + x2 = 0.3461538462 The x term is -0.3076923077x. Take half its coefficient (-0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. -0.3076923077x + 0.02366863907 + x2 = 0.3461538462 + 0.02366863907 Reorder the terms: 0.02366863907 + -0.3076923077x + x2 = 0.3461538462 + 0.02366863907 Combine like terms: 0.3461538462 + 0.02366863907 = 0.36982248527 0.02366863907 + -0.3076923077x + x2 = 0.36982248527 Factor a perfect square on the left side: (x + -0.1538461539)(x + -0.1538461539) = 0.36982248527 Calculate the square root of the right side: 0.608130319 Break this problem into two subproblems by setting (x + -0.1538461539) equal to 0.608130319 and -0.608130319.Subproblem 1
x + -0.1538461539 = 0.608130319 Simplifying x + -0.1538461539 = 0.608130319 Reorder the terms: -0.1538461539 + x = 0.608130319 Solving -0.1538461539 + x = 0.608130319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 0.608130319 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 0.608130319 + 0.1538461539 x = 0.608130319 + 0.1538461539 Combine like terms: 0.608130319 + 0.1538461539 = 0.7619764729 x = 0.7619764729 Simplifying x = 0.7619764729Subproblem 2
x + -0.1538461539 = -0.608130319 Simplifying x + -0.1538461539 = -0.608130319 Reorder the terms: -0.1538461539 + x = -0.608130319 Solving -0.1538461539 + x = -0.608130319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -0.608130319 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -0.608130319 + 0.1538461539 x = -0.608130319 + 0.1538461539 Combine like terms: -0.608130319 + 0.1538461539 = -0.4542841651 x = -0.4542841651 Simplifying x = -0.4542841651Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7619764729, -0.4542841651}
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