3x^2-7x+2x^2+5x-6=

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Solution for 3x^2-7x+2x^2+5x-6= equation:


Simplifying
3x2 + -7x + 2x2 + 5x + -6 = 0

Reorder the terms:
-6 + -7x + 5x + 3x2 + 2x2 = 0

Combine like terms: -7x + 5x = -2x
-6 + -2x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
-6 + -2x + 5x2 = 0

Solving
-6 + -2x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.2 + -0.4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.4x + x2 = 0 + 1.2
-0.4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.4x + x2 = 1.2

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 1.2 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.2 + 0.04

Combine like terms: 1.2 + 0.04 = 1.24
0.04 + -0.4x + x2 = 1.24

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.113552873 and -1.113552873.

Subproblem 1

x + -0.2 = 1.113552873 Simplifying x + -0.2 = 1.113552873 Reorder the terms: -0.2 + x = 1.113552873 Solving -0.2 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.113552873 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.113552873 + 0.2 x = 1.113552873 + 0.2 Combine like terms: 1.113552873 + 0.2 = 1.313552873 x = 1.313552873 Simplifying x = 1.313552873

Subproblem 2

x + -0.2 = -1.113552873 Simplifying x + -0.2 = -1.113552873 Reorder the terms: -0.2 + x = -1.113552873 Solving -0.2 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.113552873 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.113552873 + 0.2 x = -1.113552873 + 0.2 Combine like terms: -1.113552873 + 0.2 = -0.913552873 x = -0.913552873 Simplifying x = -0.913552873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.313552873, -0.913552873}

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