2x^2+26x^2-18x-234=0

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Solution for 2x^2+26x^2-18x-234=0 equation:


Simplifying
2x2 + 26x2 + -18x + -234 = 0

Reorder the terms:
-234 + -18x + 2x2 + 26x2 = 0

Combine like terms: 2x2 + 26x2 = 28x2
-234 + -18x + 28x2 = 0

Solving
-234 + -18x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-117 + -9x + 14x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-117 + -9x + 14x2)' equal to zero and attempt to solve: Simplifying -117 + -9x + 14x2 = 0 Solving -117 + -9x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -8.357142857 + -0.6428571429x + x2 = 0 Move the constant term to the right: Add '8.357142857' to each side of the equation. -8.357142857 + -0.6428571429x + 8.357142857 + x2 = 0 + 8.357142857 Reorder the terms: -8.357142857 + 8.357142857 + -0.6428571429x + x2 = 0 + 8.357142857 Combine like terms: -8.357142857 + 8.357142857 = 0.000000000 0.000000000 + -0.6428571429x + x2 = 0 + 8.357142857 -0.6428571429x + x2 = 0 + 8.357142857 Combine like terms: 0 + 8.357142857 = 8.357142857 -0.6428571429x + x2 = 8.357142857 The x term is -0.6428571429x. Take half its coefficient (-0.3214285715). Square it (0.1033163266) and add it to both sides. Add '0.1033163266' to each side of the equation. -0.6428571429x + 0.1033163266 + x2 = 8.357142857 + 0.1033163266 Reorder the terms: 0.1033163266 + -0.6428571429x + x2 = 8.357142857 + 0.1033163266 Combine like terms: 8.357142857 + 0.1033163266 = 8.4604591836 0.1033163266 + -0.6428571429x + x2 = 8.4604591836 Factor a perfect square on the left side: (x + -0.3214285715)(x + -0.3214285715) = 8.4604591836 Calculate the square root of the right side: 2.908686849 Break this problem into two subproblems by setting (x + -0.3214285715) equal to 2.908686849 and -2.908686849.

Subproblem 1

x + -0.3214285715 = 2.908686849 Simplifying x + -0.3214285715 = 2.908686849 Reorder the terms: -0.3214285715 + x = 2.908686849 Solving -0.3214285715 + x = 2.908686849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3214285715' to each side of the equation. -0.3214285715 + 0.3214285715 + x = 2.908686849 + 0.3214285715 Combine like terms: -0.3214285715 + 0.3214285715 = 0.0000000000 0.0000000000 + x = 2.908686849 + 0.3214285715 x = 2.908686849 + 0.3214285715 Combine like terms: 2.908686849 + 0.3214285715 = 3.2301154205 x = 3.2301154205 Simplifying x = 3.2301154205

Subproblem 2

x + -0.3214285715 = -2.908686849 Simplifying x + -0.3214285715 = -2.908686849 Reorder the terms: -0.3214285715 + x = -2.908686849 Solving -0.3214285715 + x = -2.908686849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3214285715' to each side of the equation. -0.3214285715 + 0.3214285715 + x = -2.908686849 + 0.3214285715 Combine like terms: -0.3214285715 + 0.3214285715 = 0.0000000000 0.0000000000 + x = -2.908686849 + 0.3214285715 x = -2.908686849 + 0.3214285715 Combine like terms: -2.908686849 + 0.3214285715 = -2.5872582775 x = -2.5872582775 Simplifying x = -2.5872582775

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.2301154205, -2.5872582775}

Solution

x = {3.2301154205, -2.5872582775}

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