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Simplifying 7x(x + 6) = 6 Reorder the terms: 7x(6 + x) = 6 (6 * 7x + x * 7x) = 6 (42x + 7x2) = 6 Solving 42x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 42x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 42x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 6x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 6x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 6x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + 0.8571428571 6x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 6x + x2 = 0.8571428571 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 0.8571428571 + 9 Reorder the terms: 9 + 6x + x2 = 0.8571428571 + 9 Combine like terms: 0.8571428571 + 9 = 9.8571428571 9 + 6x + x2 = 9.8571428571 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.8571428571 Calculate the square root of the right side: 3.139608711 Break this problem into two subproblems by setting (x + 3) equal to 3.139608711 and -3.139608711.Subproblem 1
x + 3 = 3.139608711 Simplifying x + 3 = 3.139608711 Reorder the terms: 3 + x = 3.139608711 Solving 3 + x = 3.139608711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.139608711 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.139608711 + -3 x = 3.139608711 + -3 Combine like terms: 3.139608711 + -3 = 0.139608711 x = 0.139608711 Simplifying x = 0.139608711Subproblem 2
x + 3 = -3.139608711 Simplifying x + 3 = -3.139608711 Reorder the terms: 3 + x = -3.139608711 Solving 3 + x = -3.139608711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.139608711 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.139608711 + -3 x = -3.139608711 + -3 Combine like terms: -3.139608711 + -3 = -6.139608711 x = -6.139608711 Simplifying x = -6.139608711Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.139608711, -6.139608711}
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