9x^2+27x-594=0

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Solution for 9x^2+27x-594=0 equation:


Simplifying
9x2 + 27x + -594 = 0

Reorder the terms:
-594 + 27x + 9x2 = 0

Solving
-594 + 27x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-66 + 3x + x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(-66 + 3x + x2)' equal to zero and attempt to solve: Simplifying -66 + 3x + x2 = 0 Solving -66 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 3x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 3x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 3x + x2 = 0 + 66 3x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 3x + x2 = 66 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 66 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 66 + 2.25 Combine like terms: 66 + 2.25 = 68.25 2.25 + 3x + x2 = 68.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 1.5) equal to 8.261355821 and -8.261355821.

Subproblem 1

x + 1.5 = 8.261355821 Simplifying x + 1.5 = 8.261355821 Reorder the terms: 1.5 + x = 8.261355821 Solving 1.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.261355821 + -1.5 x = 8.261355821 + -1.5 Combine like terms: 8.261355821 + -1.5 = 6.761355821 x = 6.761355821 Simplifying x = 6.761355821

Subproblem 2

x + 1.5 = -8.261355821 Simplifying x + 1.5 = -8.261355821 Reorder the terms: 1.5 + x = -8.261355821 Solving 1.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -8.261355821 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.261355821 + -1.5 x = -8.261355821 + -1.5 Combine like terms: -8.261355821 + -1.5 = -9.761355821 x = -9.761355821 Simplifying x = -9.761355821

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.761355821, -9.761355821}

Solution

x = {6.761355821, -9.761355821}

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