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Simplifying 11x2 + 35x = 9 Reorder the terms: 35x + 11x2 = 9 Solving 35x + 11x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 35x + 11x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 35x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.8181818182 + 3.181818182x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 3.181818182x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 3.181818182x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 3.181818182x + x2 = 0 + 0.8181818182 3.181818182x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 3.181818182x + x2 = 0.8181818182 The x term is 3.181818182x. Take half its coefficient (1.590909091). Square it (2.530991736) and add it to both sides. Add '2.530991736' to each side of the equation. 3.181818182x + 2.530991736 + x2 = 0.8181818182 + 2.530991736 Reorder the terms: 2.530991736 + 3.181818182x + x2 = 0.8181818182 + 2.530991736 Combine like terms: 0.8181818182 + 2.530991736 = 3.3491735542 2.530991736 + 3.181818182x + x2 = 3.3491735542 Factor a perfect square on the left side: (x + 1.590909091)(x + 1.590909091) = 3.3491735542 Calculate the square root of the right side: 1.83007474 Break this problem into two subproblems by setting (x + 1.590909091) equal to 1.83007474 and -1.83007474.Subproblem 1
x + 1.590909091 = 1.83007474 Simplifying x + 1.590909091 = 1.83007474 Reorder the terms: 1.590909091 + x = 1.83007474 Solving 1.590909091 + x = 1.83007474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.590909091' to each side of the equation. 1.590909091 + -1.590909091 + x = 1.83007474 + -1.590909091 Combine like terms: 1.590909091 + -1.590909091 = 0.000000000 0.000000000 + x = 1.83007474 + -1.590909091 x = 1.83007474 + -1.590909091 Combine like terms: 1.83007474 + -1.590909091 = 0.239165649 x = 0.239165649 Simplifying x = 0.239165649Subproblem 2
x + 1.590909091 = -1.83007474 Simplifying x + 1.590909091 = -1.83007474 Reorder the terms: 1.590909091 + x = -1.83007474 Solving 1.590909091 + x = -1.83007474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.590909091' to each side of the equation. 1.590909091 + -1.590909091 + x = -1.83007474 + -1.590909091 Combine like terms: 1.590909091 + -1.590909091 = 0.000000000 0.000000000 + x = -1.83007474 + -1.590909091 x = -1.83007474 + -1.590909091 Combine like terms: -1.83007474 + -1.590909091 = -3.420983831 x = -3.420983831 Simplifying x = -3.420983831Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.239165649, -3.420983831}
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