3x^2-13x-15=

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Solution for 3x^2-13x-15= equation:


Simplifying
3x2 + -13x + -15 = 0

Reorder the terms:
-15 + -13x + 3x2 = 0

Solving
-15 + -13x + 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'.
-5 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -4.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -4.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4.333333333x + x2 = 0 + 5
-4.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-4.333333333x + x2 = 5

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 5 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 5 + 4.694444446

Combine like terms: 5 + 4.694444446 = 9.694444446
4.694444446 + -4.333333333x + x2 = 9.694444446

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 9.694444446

Calculate the square root of the right side: 3.113590282

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 3.113590282 and -3.113590282.

Subproblem 1

x + -2.166666667 = 3.113590282 Simplifying x + -2.166666667 = 3.113590282 Reorder the terms: -2.166666667 + x = 3.113590282 Solving -2.166666667 + x = 3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 3.113590282 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 3.113590282 + 2.166666667 x = 3.113590282 + 2.166666667 Combine like terms: 3.113590282 + 2.166666667 = 5.280256949 x = 5.280256949 Simplifying x = 5.280256949

Subproblem 2

x + -2.166666667 = -3.113590282 Simplifying x + -2.166666667 = -3.113590282 Reorder the terms: -2.166666667 + x = -3.113590282 Solving -2.166666667 + x = -3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -3.113590282 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -3.113590282 + 2.166666667 x = -3.113590282 + 2.166666667 Combine like terms: -3.113590282 + 2.166666667 = -0.946923615 x = -0.946923615 Simplifying x = -0.946923615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.280256949, -0.946923615}

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