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Simplifying 11x2 + -75x + 36 = 0 Reorder the terms: 36 + -75x + 11x2 = 0 Solving 36 + -75x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 3.272727273 + -6.818181818x + x2 = 0 Move the constant term to the right: Add '-3.272727273' to each side of the equation. 3.272727273 + -6.818181818x + -3.272727273 + x2 = 0 + -3.272727273 Reorder the terms: 3.272727273 + -3.272727273 + -6.818181818x + x2 = 0 + -3.272727273 Combine like terms: 3.272727273 + -3.272727273 = 0.000000000 0.000000000 + -6.818181818x + x2 = 0 + -3.272727273 -6.818181818x + x2 = 0 + -3.272727273 Combine like terms: 0 + -3.272727273 = -3.272727273 -6.818181818x + x2 = -3.272727273 The x term is -6.818181818x. Take half its coefficient (-3.409090909). Square it (11.62190083) and add it to both sides. Add '11.62190083' to each side of the equation. -6.818181818x + 11.62190083 + x2 = -3.272727273 + 11.62190083 Reorder the terms: 11.62190083 + -6.818181818x + x2 = -3.272727273 + 11.62190083 Combine like terms: -3.272727273 + 11.62190083 = 8.349173557 11.62190083 + -6.818181818x + x2 = 8.349173557 Factor a perfect square on the left side: (x + -3.409090909)(x + -3.409090909) = 8.349173557 Calculate the square root of the right side: 2.889493651 Break this problem into two subproblems by setting (x + -3.409090909) equal to 2.889493651 and -2.889493651.Subproblem 1
x + -3.409090909 = 2.889493651 Simplifying x + -3.409090909 = 2.889493651 Reorder the terms: -3.409090909 + x = 2.889493651 Solving -3.409090909 + x = 2.889493651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.409090909' to each side of the equation. -3.409090909 + 3.409090909 + x = 2.889493651 + 3.409090909 Combine like terms: -3.409090909 + 3.409090909 = 0.000000000 0.000000000 + x = 2.889493651 + 3.409090909 x = 2.889493651 + 3.409090909 Combine like terms: 2.889493651 + 3.409090909 = 6.29858456 x = 6.29858456 Simplifying x = 6.29858456Subproblem 2
x + -3.409090909 = -2.889493651 Simplifying x + -3.409090909 = -2.889493651 Reorder the terms: -3.409090909 + x = -2.889493651 Solving -3.409090909 + x = -2.889493651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.409090909' to each side of the equation. -3.409090909 + 3.409090909 + x = -2.889493651 + 3.409090909 Combine like terms: -3.409090909 + 3.409090909 = 0.000000000 0.000000000 + x = -2.889493651 + 3.409090909 x = -2.889493651 + 3.409090909 Combine like terms: -2.889493651 + 3.409090909 = 0.519597258 x = 0.519597258 Simplifying x = 0.519597258Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.29858456, 0.519597258}
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