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Simplifying 13x2 + 25x + -254 = 0 Reorder the terms: -254 + 25x + 13x2 = 0 Solving -254 + 25x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -19.53846154 + 1.923076923x + x2 = 0 Move the constant term to the right: Add '19.53846154' to each side of the equation. -19.53846154 + 1.923076923x + 19.53846154 + x2 = 0 + 19.53846154 Reorder the terms: -19.53846154 + 19.53846154 + 1.923076923x + x2 = 0 + 19.53846154 Combine like terms: -19.53846154 + 19.53846154 = 0.00000000 0.00000000 + 1.923076923x + x2 = 0 + 19.53846154 1.923076923x + x2 = 0 + 19.53846154 Combine like terms: 0 + 19.53846154 = 19.53846154 1.923076923x + x2 = 19.53846154 The x term is 1.923076923x. Take half its coefficient (0.9615384615). Square it (0.9245562129) and add it to both sides. Add '0.9245562129' to each side of the equation. 1.923076923x + 0.9245562129 + x2 = 19.53846154 + 0.9245562129 Reorder the terms: 0.9245562129 + 1.923076923x + x2 = 19.53846154 + 0.9245562129 Combine like terms: 19.53846154 + 0.9245562129 = 20.4630177529 0.9245562129 + 1.923076923x + x2 = 20.4630177529 Factor a perfect square on the left side: (x + 0.9615384615)(x + 0.9615384615) = 20.4630177529 Calculate the square root of the right side: 4.52360672 Break this problem into two subproblems by setting (x + 0.9615384615) equal to 4.52360672 and -4.52360672.Subproblem 1
x + 0.9615384615 = 4.52360672 Simplifying x + 0.9615384615 = 4.52360672 Reorder the terms: 0.9615384615 + x = 4.52360672 Solving 0.9615384615 + x = 4.52360672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9615384615' to each side of the equation. 0.9615384615 + -0.9615384615 + x = 4.52360672 + -0.9615384615 Combine like terms: 0.9615384615 + -0.9615384615 = 0.0000000000 0.0000000000 + x = 4.52360672 + -0.9615384615 x = 4.52360672 + -0.9615384615 Combine like terms: 4.52360672 + -0.9615384615 = 3.5620682585 x = 3.5620682585 Simplifying x = 3.5620682585Subproblem 2
x + 0.9615384615 = -4.52360672 Simplifying x + 0.9615384615 = -4.52360672 Reorder the terms: 0.9615384615 + x = -4.52360672 Solving 0.9615384615 + x = -4.52360672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9615384615' to each side of the equation. 0.9615384615 + -0.9615384615 + x = -4.52360672 + -0.9615384615 Combine like terms: 0.9615384615 + -0.9615384615 = 0.0000000000 0.0000000000 + x = -4.52360672 + -0.9615384615 x = -4.52360672 + -0.9615384615 Combine like terms: -4.52360672 + -0.9615384615 = -5.4851451815 x = -5.4851451815 Simplifying x = -5.4851451815Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5620682585, -5.4851451815}
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