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Simplifying 6x(x + 7) = 6x + -7 Reorder the terms: 6x(7 + x) = 6x + -7 (7 * 6x + x * 6x) = 6x + -7 (42x + 6x2) = 6x + -7 Reorder the terms: 42x + 6x2 = -7 + 6x Solving 42x + 6x2 = -7 + 6x Solving for variable 'x'. Reorder the terms: 7 + 42x + -6x + 6x2 = -7 + 6x + 7 + -6x Combine like terms: 42x + -6x = 36x 7 + 36x + 6x2 = -7 + 6x + 7 + -6x Reorder the terms: 7 + 36x + 6x2 = -7 + 7 + 6x + -6x Combine like terms: -7 + 7 = 0 7 + 36x + 6x2 = 0 + 6x + -6x 7 + 36x + 6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 7 + 36x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 6x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 6x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 6x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + -1.166666667 6x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 6x + x2 = -1.166666667 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 = -1.166666667 + 9 Reorder the terms: 9 + 6x + x2 = -1.166666667 + 9 Combine like terms: -1.166666667 + 9 = 7.833333333 9 + 6x + x2 = 7.833333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 7.833333333 Calculate the square root of the right side: 2.798809271 Break this problem into two subproblems by setting (x + 3) equal to 2.798809271 and -2.798809271.Subproblem 1
x + 3 = 2.798809271 Simplifying x + 3 = 2.798809271 Reorder the terms: 3 + x = 2.798809271 Solving 3 + x = 2.798809271 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 = 2.798809271 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.798809271 + -3 x = 2.798809271 + -3 Combine like terms: 2.798809271 + -3 = -0.201190729 x = -0.201190729 Simplifying x = -0.201190729Subproblem 2
x + 3 = -2.798809271 Simplifying x + 3 = -2.798809271 Reorder the terms: 3 + x = -2.798809271 Solving 3 + x = -2.798809271 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 = -2.798809271 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.798809271 + -3 x = -2.798809271 + -3 Combine like terms: -2.798809271 + -3 = -5.798809271 x = -5.798809271 Simplifying x = -5.798809271Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.201190729, -5.798809271}
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