18x^2+24x+264=1000

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Solution for 18x^2+24x+264=1000 equation:


Simplifying
18x2 + 24x + 264 = 1000

Reorder the terms:
264 + 24x + 18x2 = 1000

Solving
264 + 24x + 18x2 = 1000

Solving for variable 'x'.

Reorder the terms:
264 + -1000 + 24x + 18x2 = 1000 + -1000

Combine like terms: 264 + -1000 = -736
-736 + 24x + 18x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-736 + 24x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-368 + 12x + 9x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-368 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying -368 + 12x + 9x2 = 0 Solving -368 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -40.88888889 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '40.88888889' to each side of the equation. -40.88888889 + 1.333333333x + 40.88888889 + x2 = 0 + 40.88888889 Reorder the terms: -40.88888889 + 40.88888889 + 1.333333333x + x2 = 0 + 40.88888889 Combine like terms: -40.88888889 + 40.88888889 = 0.00000000 0.00000000 + 1.333333333x + x2 = 0 + 40.88888889 1.333333333x + x2 = 0 + 40.88888889 Combine like terms: 0 + 40.88888889 = 40.88888889 1.333333333x + x2 = 40.88888889 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 40.88888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 40.88888889 + 0.4444444442 Combine like terms: 40.88888889 + 0.4444444442 = 41.3333333342 0.4444444442 + 1.333333333x + x2 = 41.3333333342 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 41.3333333342 Calculate the square root of the right side: 6.429100507 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 6.429100507 and -6.429100507.

Subproblem 1

x + 0.6666666665 = 6.429100507 Simplifying x + 0.6666666665 = 6.429100507 Reorder the terms: 0.6666666665 + x = 6.429100507 Solving 0.6666666665 + x = 6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 6.429100507 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 6.429100507 + -0.6666666665 x = 6.429100507 + -0.6666666665 Combine like terms: 6.429100507 + -0.6666666665 = 5.7624338405 x = 5.7624338405 Simplifying x = 5.7624338405

Subproblem 2

x + 0.6666666665 = -6.429100507 Simplifying x + 0.6666666665 = -6.429100507 Reorder the terms: 0.6666666665 + x = -6.429100507 Solving 0.6666666665 + x = -6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -6.429100507 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -6.429100507 + -0.6666666665 x = -6.429100507 + -0.6666666665 Combine like terms: -6.429100507 + -0.6666666665 = -7.0957671735 x = -7.0957671735 Simplifying x = -7.0957671735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.7624338405, -7.0957671735}

Solution

x = {5.7624338405, -7.0957671735}

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