18x^2-16x-6=0

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Solution for 18x^2-16x-6=0 equation:


Simplifying
18x2 + -16x + -6 = 0

Reorder the terms:
-6 + -16x + 18x2 = 0

Solving
-6 + -16x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -8x + 9x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -8x + 9x2)' equal to zero and attempt to solve: Simplifying -3 + -8x + 9x2 = 0 Solving -3 + -8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.8888888889x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.3333333333 -0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.8888888889x + x2 = 0.3333333333 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.3333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.3333333333 + 0.1975308642 Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975 0.1975308642 + -0.8888888889x + x2 = 0.5308641975 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.5308641975 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.72860428 and -0.72860428.

Subproblem 1

x + -0.4444444445 = 0.72860428 Simplifying x + -0.4444444445 = 0.72860428 Reorder the terms: -0.4444444445 + x = 0.72860428 Solving -0.4444444445 + x = 0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.72860428 + 0.4444444445 x = 0.72860428 + 0.4444444445 Combine like terms: 0.72860428 + 0.4444444445 = 1.1730487245 x = 1.1730487245 Simplifying x = 1.1730487245

Subproblem 2

x + -0.4444444445 = -0.72860428 Simplifying x + -0.4444444445 = -0.72860428 Reorder the terms: -0.4444444445 + x = -0.72860428 Solving -0.4444444445 + x = -0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.72860428 + 0.4444444445 x = -0.72860428 + 0.4444444445 Combine like terms: -0.72860428 + 0.4444444445 = -0.2841598355 x = -0.2841598355 Simplifying x = -0.2841598355

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1730487245, -0.2841598355}

Solution

x = {1.1730487245, -0.2841598355}

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