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Simplifying 26x2 + -30x + -25 = 0 Reorder the terms: -25 + -30x + 26x2 = 0 Solving -25 + -30x + 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'. -0.9615384615 + -1.153846154x + x2 = 0 Move the constant term to the right: Add '0.9615384615' to each side of the equation. -0.9615384615 + -1.153846154x + 0.9615384615 + x2 = 0 + 0.9615384615 Reorder the terms: -0.9615384615 + 0.9615384615 + -1.153846154x + x2 = 0 + 0.9615384615 Combine like terms: -0.9615384615 + 0.9615384615 = 0.0000000000 0.0000000000 + -1.153846154x + x2 = 0 + 0.9615384615 -1.153846154x + x2 = 0 + 0.9615384615 Combine like terms: 0 + 0.9615384615 = 0.9615384615 -1.153846154x + x2 = 0.9615384615 The x term is -1.153846154x. Take half its coefficient (-0.576923077). Square it (0.3328402368) and add it to both sides. Add '0.3328402368' to each side of the equation. -1.153846154x + 0.3328402368 + x2 = 0.9615384615 + 0.3328402368 Reorder the terms: 0.3328402368 + -1.153846154x + x2 = 0.9615384615 + 0.3328402368 Combine like terms: 0.9615384615 + 0.3328402368 = 1.2943786983 0.3328402368 + -1.153846154x + x2 = 1.2943786983 Factor a perfect square on the left side: (x + -0.576923077)(x + -0.576923077) = 1.2943786983 Calculate the square root of the right side: 1.137707651 Break this problem into two subproblems by setting (x + -0.576923077) equal to 1.137707651 and -1.137707651.Subproblem 1
x + -0.576923077 = 1.137707651 Simplifying x + -0.576923077 = 1.137707651 Reorder the terms: -0.576923077 + x = 1.137707651 Solving -0.576923077 + x = 1.137707651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = 1.137707651 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = 1.137707651 + 0.576923077 x = 1.137707651 + 0.576923077 Combine like terms: 1.137707651 + 0.576923077 = 1.714630728 x = 1.714630728 Simplifying x = 1.714630728Subproblem 2
x + -0.576923077 = -1.137707651 Simplifying x + -0.576923077 = -1.137707651 Reorder the terms: -0.576923077 + x = -1.137707651 Solving -0.576923077 + x = -1.137707651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.576923077' to each side of the equation. -0.576923077 + 0.576923077 + x = -1.137707651 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = -1.137707651 + 0.576923077 x = -1.137707651 + 0.576923077 Combine like terms: -1.137707651 + 0.576923077 = -0.560784574 x = -0.560784574 Simplifying x = -0.560784574Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.714630728, -0.560784574}
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