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Simplifying -6x(9x + 5) + -3x + 4x = -408 + 8 Reorder the terms: -6x(5 + 9x) + -3x + 4x = -408 + 8 (5 * -6x + 9x * -6x) + -3x + 4x = -408 + 8 (-30x + -54x2) + -3x + 4x = -408 + 8 Reorder the terms: -30x + -3x + 4x + -54x2 = -408 + 8 Combine like terms: -30x + -3x = -33x -33x + 4x + -54x2 = -408 + 8 Combine like terms: -33x + 4x = -29x -29x + -54x2 = -408 + 8 Combine like terms: -408 + 8 = -400 -29x + -54x2 = -400 Solving -29x + -54x2 = -400 Solving for variable 'x'. Reorder the terms: 400 + -29x + -54x2 = -400 + 400 Combine like terms: -400 + 400 = 0 400 + -29x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. -7.407407407 + 0.537037037x + x2 = 0 Move the constant term to the right: Add '7.407407407' to each side of the equation. -7.407407407 + 0.537037037x + 7.407407407 + x2 = 0 + 7.407407407 Reorder the terms: -7.407407407 + 7.407407407 + 0.537037037x + x2 = 0 + 7.407407407 Combine like terms: -7.407407407 + 7.407407407 = 0.000000000 0.000000000 + 0.537037037x + x2 = 0 + 7.407407407 0.537037037x + x2 = 0 + 7.407407407 Combine like terms: 0 + 7.407407407 = 7.407407407 0.537037037x + x2 = 7.407407407 The x term is 0.537037037x. Take half its coefficient (0.2685185185). Square it (0.07210219478) and add it to both sides. Add '0.07210219478' to each side of the equation. 0.537037037x + 0.07210219478 + x2 = 7.407407407 + 0.07210219478 Reorder the terms: 0.07210219478 + 0.537037037x + x2 = 7.407407407 + 0.07210219478 Combine like terms: 7.407407407 + 0.07210219478 = 7.47950960178 0.07210219478 + 0.537037037x + x2 = 7.47950960178 Factor a perfect square on the left side: (x + 0.2685185185)(x + 0.2685185185) = 7.47950960178 Calculate the square root of the right side: 2.734869211 Break this problem into two subproblems by setting (x + 0.2685185185) equal to 2.734869211 and -2.734869211.Subproblem 1
x + 0.2685185185 = 2.734869211 Simplifying x + 0.2685185185 = 2.734869211 Reorder the terms: 0.2685185185 + x = 2.734869211 Solving 0.2685185185 + x = 2.734869211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2685185185' to each side of the equation. 0.2685185185 + -0.2685185185 + x = 2.734869211 + -0.2685185185 Combine like terms: 0.2685185185 + -0.2685185185 = 0.0000000000 0.0000000000 + x = 2.734869211 + -0.2685185185 x = 2.734869211 + -0.2685185185 Combine like terms: 2.734869211 + -0.2685185185 = 2.4663506925 x = 2.4663506925 Simplifying x = 2.4663506925Subproblem 2
x + 0.2685185185 = -2.734869211 Simplifying x + 0.2685185185 = -2.734869211 Reorder the terms: 0.2685185185 + x = -2.734869211 Solving 0.2685185185 + x = -2.734869211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2685185185' to each side of the equation. 0.2685185185 + -0.2685185185 + x = -2.734869211 + -0.2685185185 Combine like terms: 0.2685185185 + -0.2685185185 = 0.0000000000 0.0000000000 + x = -2.734869211 + -0.2685185185 x = -2.734869211 + -0.2685185185 Combine like terms: -2.734869211 + -0.2685185185 = -3.0033877295 x = -3.0033877295 Simplifying x = -3.0033877295Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4663506925, -3.0033877295}
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