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Simplifying (5x2 + -7x + -26) + (6x2 + 9x) = 0 Reorder the terms: (-26 + -7x + 5x2) + (6x2 + 9x) = 0 Remove parenthesis around (-26 + -7x + 5x2) -26 + -7x + 5x2 + (6x2 + 9x) = 0 Reorder the terms: -26 + -7x + 5x2 + (9x + 6x2) = 0 Remove parenthesis around (9x + 6x2) -26 + -7x + 5x2 + 9x + 6x2 = 0 Reorder the terms: -26 + -7x + 9x + 5x2 + 6x2 = 0 Combine like terms: -7x + 9x = 2x -26 + 2x + 5x2 + 6x2 = 0 Combine like terms: 5x2 + 6x2 = 11x2 -26 + 2x + 11x2 = 0 Solving -26 + 2x + 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'. -2.363636364 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '2.363636364' to each side of the equation. -2.363636364 + 0.1818181818x + 2.363636364 + x2 = 0 + 2.363636364 Reorder the terms: -2.363636364 + 2.363636364 + 0.1818181818x + x2 = 0 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + 0.1818181818x + x2 = 0 + 2.363636364 0.1818181818x + x2 = 0 + 2.363636364 Combine like terms: 0 + 2.363636364 = 2.363636364 0.1818181818x + x2 = 2.363636364 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 2.363636364 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 2.363636364 + 0.008264462808 Combine like terms: 2.363636364 + 0.008264462808 = 2.371900826808 0.008264462808 + 0.1818181818x + x2 = 2.371900826808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 2.371900826808 Calculate the square root of the right side: 1.540097668 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.540097668 and -1.540097668.Subproblem 1
x + 0.0909090909 = 1.540097668 Simplifying x + 0.0909090909 = 1.540097668 Reorder the terms: 0.0909090909 + x = 1.540097668 Solving 0.0909090909 + x = 1.540097668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 1.540097668 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.540097668 + -0.0909090909 x = 1.540097668 + -0.0909090909 Combine like terms: 1.540097668 + -0.0909090909 = 1.4491885771 x = 1.4491885771 Simplifying x = 1.4491885771Subproblem 2
x + 0.0909090909 = -1.540097668 Simplifying x + 0.0909090909 = -1.540097668 Reorder the terms: 0.0909090909 + x = -1.540097668 Solving 0.0909090909 + x = -1.540097668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -1.540097668 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.540097668 + -0.0909090909 x = -1.540097668 + -0.0909090909 Combine like terms: -1.540097668 + -0.0909090909 = -1.6310067589 x = -1.6310067589 Simplifying x = -1.6310067589Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4491885771, -1.6310067589}
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