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Simplifying -6x(9x + 5) + -3x + 4x = -408 + x Reorder the terms: -6x(5 + 9x) + -3x + 4x = -408 + x (5 * -6x + 9x * -6x) + -3x + 4x = -408 + x (-30x + -54x2) + -3x + 4x = -408 + x Reorder the terms: -30x + -3x + 4x + -54x2 = -408 + x Combine like terms: -30x + -3x = -33x -33x + 4x + -54x2 = -408 + x Combine like terms: -33x + 4x = -29x -29x + -54x2 = -408 + x Solving -29x + -54x2 = -408 + x Solving for variable 'x'. Reorder the terms: 408 + -29x + -1x + -54x2 = -408 + x + 408 + -1x Combine like terms: -29x + -1x = -30x 408 + -30x + -54x2 = -408 + x + 408 + -1x Reorder the terms: 408 + -30x + -54x2 = -408 + 408 + x + -1x Combine like terms: -408 + 408 = 0 408 + -30x + -54x2 = 0 + x + -1x 408 + -30x + -54x2 = x + -1x Combine like terms: x + -1x = 0 408 + -30x + -54x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(68 + -5x + -9x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(68 + -5x + -9x2)' equal to zero and attempt to solve: Simplifying 68 + -5x + -9x2 = 0 Solving 68 + -5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -7.555555556 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '7.555555556' to each side of the equation. -7.555555556 + 0.5555555556x + 7.555555556 + x2 = 0 + 7.555555556 Reorder the terms: -7.555555556 + 7.555555556 + 0.5555555556x + x2 = 0 + 7.555555556 Combine like terms: -7.555555556 + 7.555555556 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 7.555555556 0.5555555556x + x2 = 0 + 7.555555556 Combine like terms: 0 + 7.555555556 = 7.555555556 0.5555555556x + x2 = 7.555555556 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 7.555555556 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 7.555555556 + 0.07716049384 Combine like terms: 7.555555556 + 0.07716049384 = 7.63271604984 0.07716049384 + 0.5555555556x + x2 = 7.63271604984 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 7.63271604984 Calculate the square root of the right side: 2.762737058 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 2.762737058 and -2.762737058.Subproblem 1
x + 0.2777777778 = 2.762737058 Simplifying x + 0.2777777778 = 2.762737058 Reorder the terms: 0.2777777778 + x = 2.762737058 Solving 0.2777777778 + x = 2.762737058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 2.762737058 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 2.762737058 + -0.2777777778 x = 2.762737058 + -0.2777777778 Combine like terms: 2.762737058 + -0.2777777778 = 2.4849592802 x = 2.4849592802 Simplifying x = 2.4849592802Subproblem 2
x + 0.2777777778 = -2.762737058 Simplifying x + 0.2777777778 = -2.762737058 Reorder the terms: 0.2777777778 + x = -2.762737058 Solving 0.2777777778 + x = -2.762737058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -2.762737058 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -2.762737058 + -0.2777777778 x = -2.762737058 + -0.2777777778 Combine like terms: -2.762737058 + -0.2777777778 = -3.0405148358 x = -3.0405148358 Simplifying x = -3.0405148358Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4849592802, -3.0405148358}Solution
x = {2.4849592802, -3.0405148358}
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