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Simplifying 3 + 5x(6 + 3x) + -7x + 4(9x + 3) = 0 3 + (6 * 5x + 3x * 5x) + -7x + 4(9x + 3) = 0 3 + (30x + 15x2) + -7x + 4(9x + 3) = 0 Reorder the terms: 3 + 30x + 15x2 + -7x + 4(3 + 9x) = 0 3 + 30x + 15x2 + -7x + (3 * 4 + 9x * 4) = 0 3 + 30x + 15x2 + -7x + (12 + 36x) = 0 Reorder the terms: 3 + 12 + 30x + -7x + 36x + 15x2 = 0 Combine like terms: 3 + 12 = 15 15 + 30x + -7x + 36x + 15x2 = 0 Combine like terms: 30x + -7x = 23x 15 + 23x + 36x + 15x2 = 0 Combine like terms: 23x + 36x = 59x 15 + 59x + 15x2 = 0 Solving 15 + 59x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1 + 3.933333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3.933333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3.933333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3.933333333x + x2 = 0 + -1 3.933333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3.933333333x + x2 = -1 The x term is 3.933333333x. Take half its coefficient (1.966666667). Square it (3.867777779) and add it to both sides. Add '3.867777779' to each side of the equation. 3.933333333x + 3.867777779 + x2 = -1 + 3.867777779 Reorder the terms: 3.867777779 + 3.933333333x + x2 = -1 + 3.867777779 Combine like terms: -1 + 3.867777779 = 2.867777779 3.867777779 + 3.933333333x + x2 = 2.867777779 Factor a perfect square on the left side: (x + 1.966666667)(x + 1.966666667) = 2.867777779 Calculate the square root of the right side: 1.69345144 Break this problem into two subproblems by setting (x + 1.966666667) equal to 1.69345144 and -1.69345144.Subproblem 1
x + 1.966666667 = 1.69345144 Simplifying x + 1.966666667 = 1.69345144 Reorder the terms: 1.966666667 + x = 1.69345144 Solving 1.966666667 + x = 1.69345144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.966666667' to each side of the equation. 1.966666667 + -1.966666667 + x = 1.69345144 + -1.966666667 Combine like terms: 1.966666667 + -1.966666667 = 0.000000000 0.000000000 + x = 1.69345144 + -1.966666667 x = 1.69345144 + -1.966666667 Combine like terms: 1.69345144 + -1.966666667 = -0.273215227 x = -0.273215227 Simplifying x = -0.273215227Subproblem 2
x + 1.966666667 = -1.69345144 Simplifying x + 1.966666667 = -1.69345144 Reorder the terms: 1.966666667 + x = -1.69345144 Solving 1.966666667 + x = -1.69345144 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.966666667' to each side of the equation. 1.966666667 + -1.966666667 + x = -1.69345144 + -1.966666667 Combine like terms: 1.966666667 + -1.966666667 = 0.000000000 0.000000000 + x = -1.69345144 + -1.966666667 x = -1.69345144 + -1.966666667 Combine like terms: -1.69345144 + -1.966666667 = -3.660118107 x = -3.660118107 Simplifying x = -3.660118107Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.273215227, -3.660118107}
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