3x^2+8x-95=0

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Solution for 3x^2+8x-95=0 equation:


Simplifying
3x2 + 8x + -95 = 0

Reorder the terms:
-95 + 8x + 3x2 = 0

Solving
-95 + 8x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-31.66666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '31.66666667' to each side of the equation.
-31.66666667 + 2.666666667x + 31.66666667 + x2 = 0 + 31.66666667

Reorder the terms:
-31.66666667 + 31.66666667 + 2.666666667x + x2 = 0 + 31.66666667

Combine like terms: -31.66666667 + 31.66666667 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 31.66666667
2.666666667x + x2 = 0 + 31.66666667

Combine like terms: 0 + 31.66666667 = 31.66666667
2.666666667x + x2 = 31.66666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 31.66666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 31.66666667 + 1.777777780

Combine like terms: 31.66666667 + 1.777777780 = 33.44444445
1.777777780 + 2.666666667x + x2 = 33.44444445

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 33.44444445

Calculate the square root of the right side: 5.783117191

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 5.783117191 and -5.783117191.

Subproblem 1

x + 1.333333334 = 5.783117191 Simplifying x + 1.333333334 = 5.783117191 Reorder the terms: 1.333333334 + x = 5.783117191 Solving 1.333333334 + x = 5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 5.783117191 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.783117191 + -1.333333334 x = 5.783117191 + -1.333333334 Combine like terms: 5.783117191 + -1.333333334 = 4.449783857 x = 4.449783857 Simplifying x = 4.449783857

Subproblem 2

x + 1.333333334 = -5.783117191 Simplifying x + 1.333333334 = -5.783117191 Reorder the terms: 1.333333334 + x = -5.783117191 Solving 1.333333334 + x = -5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -5.783117191 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.783117191 + -1.333333334 x = -5.783117191 + -1.333333334 Combine like terms: -5.783117191 + -1.333333334 = -7.116450525 x = -7.116450525 Simplifying x = -7.116450525

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.449783857, -7.116450525}

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