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Simplifying 26x2 + -30x + -1147 = 0 Reorder the terms: -1147 + -30x + 26x2 = 0 Solving -1147 + -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'. -44.11538462 + -1.153846154x + x2 = 0 Move the constant term to the right: Add '44.11538462' to each side of the equation. -44.11538462 + -1.153846154x + 44.11538462 + x2 = 0 + 44.11538462 Reorder the terms: -44.11538462 + 44.11538462 + -1.153846154x + x2 = 0 + 44.11538462 Combine like terms: -44.11538462 + 44.11538462 = 0.00000000 0.00000000 + -1.153846154x + x2 = 0 + 44.11538462 -1.153846154x + x2 = 0 + 44.11538462 Combine like terms: 0 + 44.11538462 = 44.11538462 -1.153846154x + x2 = 44.11538462 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 = 44.11538462 + 0.3328402368 Reorder the terms: 0.3328402368 + -1.153846154x + x2 = 44.11538462 + 0.3328402368 Combine like terms: 44.11538462 + 0.3328402368 = 44.4482248568 0.3328402368 + -1.153846154x + x2 = 44.4482248568 Factor a perfect square on the left side: (x + -0.576923077)(x + -0.576923077) = 44.4482248568 Calculate the square root of the right side: 6.666950192 Break this problem into two subproblems by setting (x + -0.576923077) equal to 6.666950192 and -6.666950192.Subproblem 1
x + -0.576923077 = 6.666950192 Simplifying x + -0.576923077 = 6.666950192 Reorder the terms: -0.576923077 + x = 6.666950192 Solving -0.576923077 + x = 6.666950192 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 = 6.666950192 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = 6.666950192 + 0.576923077 x = 6.666950192 + 0.576923077 Combine like terms: 6.666950192 + 0.576923077 = 7.243873269 x = 7.243873269 Simplifying x = 7.243873269Subproblem 2
x + -0.576923077 = -6.666950192 Simplifying x + -0.576923077 = -6.666950192 Reorder the terms: -0.576923077 + x = -6.666950192 Solving -0.576923077 + x = -6.666950192 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 = -6.666950192 + 0.576923077 Combine like terms: -0.576923077 + 0.576923077 = 0.000000000 0.000000000 + x = -6.666950192 + 0.576923077 x = -6.666950192 + 0.576923077 Combine like terms: -6.666950192 + 0.576923077 = -6.090027115 x = -6.090027115 Simplifying x = -6.090027115Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.243873269, -6.090027115}
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