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Simplifying 3(x + 7) * x = -2 Reorder the terms: 3(7 + x) * x = -2 Reorder the terms for easier multiplication: 3x(7 + x) = -2 (7 * 3x + x * 3x) = -2 (21x + 3x2) = -2 Solving 21x + 3x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 21x + 3x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 21x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 7x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 7x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 7x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 7x + x2 = 0 + -0.6666666667 7x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 7x + x2 = -0.6666666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -0.6666666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -0.6666666667 + 12.25 Combine like terms: -0.6666666667 + 12.25 = 11.5833333333 12.25 + 7x + x2 = 11.5833333333 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.5833333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (x + 3.5) equal to 3.403429643 and -3.403429643.Subproblem 1
x + 3.5 = 3.403429643 Simplifying x + 3.5 = 3.403429643 Reorder the terms: 3.5 + x = 3.403429643 Solving 3.5 + x = 3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.403429643 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.403429643 + -3.5 x = 3.403429643 + -3.5 Combine like terms: 3.403429643 + -3.5 = -0.096570357 x = -0.096570357 Simplifying x = -0.096570357Subproblem 2
x + 3.5 = -3.403429643 Simplifying x + 3.5 = -3.403429643 Reorder the terms: 3.5 + x = -3.403429643 Solving 3.5 + x = -3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.403429643 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.403429643 + -3.5 x = -3.403429643 + -3.5 Combine like terms: -3.403429643 + -3.5 = -6.903429643 x = -6.903429643 Simplifying x = -6.903429643Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.096570357, -6.903429643}
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