36x^2-98x-12=0

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Solution for 36x^2-98x-12=0 equation:


Simplifying
36x2 + -98x + -12 = 0

Reorder the terms:
-12 + -98x + 36x2 = 0

Solving
-12 + -98x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -49x + 18x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-6 + -49x + 18x2)' equal to zero and attempt to solve: Simplifying -6 + -49x + 18x2 = 0 Solving -6 + -49x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.3333333333 + -2.722222222x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -2.722222222x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -2.722222222x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -2.722222222x + x2 = 0 + 0.3333333333 -2.722222222x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -2.722222222x + x2 = 0.3333333333 The x term is -2.722222222x. Take half its coefficient (-1.361111111). Square it (1.852623456) and add it to both sides. Add '1.852623456' to each side of the equation. -2.722222222x + 1.852623456 + x2 = 0.3333333333 + 1.852623456 Reorder the terms: 1.852623456 + -2.722222222x + x2 = 0.3333333333 + 1.852623456 Combine like terms: 0.3333333333 + 1.852623456 = 2.1859567893 1.852623456 + -2.722222222x + x2 = 2.1859567893 Factor a perfect square on the left side: (x + -1.361111111)(x + -1.361111111) = 2.1859567893 Calculate the square root of the right side: 1.478498153 Break this problem into two subproblems by setting (x + -1.361111111) equal to 1.478498153 and -1.478498153.

Subproblem 1

x + -1.361111111 = 1.478498153 Simplifying x + -1.361111111 = 1.478498153 Reorder the terms: -1.361111111 + x = 1.478498153 Solving -1.361111111 + x = 1.478498153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.361111111' to each side of the equation. -1.361111111 + 1.361111111 + x = 1.478498153 + 1.361111111 Combine like terms: -1.361111111 + 1.361111111 = 0.000000000 0.000000000 + x = 1.478498153 + 1.361111111 x = 1.478498153 + 1.361111111 Combine like terms: 1.478498153 + 1.361111111 = 2.839609264 x = 2.839609264 Simplifying x = 2.839609264

Subproblem 2

x + -1.361111111 = -1.478498153 Simplifying x + -1.361111111 = -1.478498153 Reorder the terms: -1.361111111 + x = -1.478498153 Solving -1.361111111 + x = -1.478498153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.361111111' to each side of the equation. -1.361111111 + 1.361111111 + x = -1.478498153 + 1.361111111 Combine like terms: -1.361111111 + 1.361111111 = 0.000000000 0.000000000 + x = -1.478498153 + 1.361111111 x = -1.478498153 + 1.361111111 Combine like terms: -1.478498153 + 1.361111111 = -0.117387042 x = -0.117387042 Simplifying x = -0.117387042

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.839609264, -0.117387042}

Solution

x = {2.839609264, -0.117387042}

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