2(6x^2-35x-72)=0

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Solution for 2(6x^2-35x-72)=0 equation:


Simplifying
2(6x2 + -35x + -72) = 0

Reorder the terms:
2(-72 + -35x + 6x2) = 0
(-72 * 2 + -35x * 2 + 6x2 * 2) = 0
(-144 + -70x + 12x2) = 0

Solving
-144 + -70x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -35x + 6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-72 + -35x + 6x2)' equal to zero and attempt to solve: Simplifying -72 + -35x + 6x2 = 0 Solving -72 + -35x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12 + -5.833333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -5.833333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -5.833333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5.833333333x + x2 = 0 + 12 -5.833333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5.833333333x + x2 = 12 The x term is -5.833333333x. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333x + 8.506944446 + x2 = 12 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333x + x2 = 12 + 8.506944446 Combine like terms: 12 + 8.506944446 = 20.506944446 8.506944446 + -5.833333333x + x2 = 20.506944446 Factor a perfect square on the left side: (x + -2.916666667)(x + -2.916666667) = 20.506944446 Calculate the square root of the right side: 4.52845939 Break this problem into two subproblems by setting (x + -2.916666667) equal to 4.52845939 and -4.52845939.

Subproblem 1

x + -2.916666667 = 4.52845939 Simplifying x + -2.916666667 = 4.52845939 Reorder the terms: -2.916666667 + x = 4.52845939 Solving -2.916666667 + x = 4.52845939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 4.52845939 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 4.52845939 + 2.916666667 x = 4.52845939 + 2.916666667 Combine like terms: 4.52845939 + 2.916666667 = 7.445126057 x = 7.445126057 Simplifying x = 7.445126057

Subproblem 2

x + -2.916666667 = -4.52845939 Simplifying x + -2.916666667 = -4.52845939 Reorder the terms: -2.916666667 + x = -4.52845939 Solving -2.916666667 + x = -4.52845939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -4.52845939 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -4.52845939 + 2.916666667 x = -4.52845939 + 2.916666667 Combine like terms: -4.52845939 + 2.916666667 = -1.611792723 x = -1.611792723 Simplifying x = -1.611792723

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.445126057, -1.611792723}

Solution

x = {7.445126057, -1.611792723}

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