(4x^2-9x-7)-(3x^2-5x-6)=0

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Solution for (4x^2-9x-7)-(3x^2-5x-6)=0 equation:


Simplifying
(4x2 + -9x + -7) + -1(3x2 + -5x + -6) = 0

Reorder the terms:
(-7 + -9x + 4x2) + -1(3x2 + -5x + -6) = 0

Remove parenthesis around (-7 + -9x + 4x2)
-7 + -9x + 4x2 + -1(3x2 + -5x + -6) = 0

Reorder the terms:
-7 + -9x + 4x2 + -1(-6 + -5x + 3x2) = 0
-7 + -9x + 4x2 + (-6 * -1 + -5x * -1 + 3x2 * -1) = 0
-7 + -9x + 4x2 + (6 + 5x + -3x2) = 0

Reorder the terms:
-7 + 6 + -9x + 5x + 4x2 + -3x2 = 0

Combine like terms: -7 + 6 = -1
-1 + -9x + 5x + 4x2 + -3x2 = 0

Combine like terms: -9x + 5x = -4x
-1 + -4x + 4x2 + -3x2 = 0

Combine like terms: 4x2 + -3x2 = 1x2
-1 + -4x + 1x2 = 0

Solving
-1 + -4x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x + x2 = 0 + 1
-4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4x + x2 = 1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + -4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -2 = 2.236067978 Simplifying x + -2 = 2.236067978 Reorder the terms: -2 + x = 2.236067978 Solving -2 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.236067978 + 2 x = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 x = 4.236067978 Simplifying x = 4.236067978

Subproblem 2

x + -2 = -2.236067978 Simplifying x + -2 = -2.236067978 Reorder the terms: -2 + x = -2.236067978 Solving -2 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.236067978 + 2 x = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 x = -0.236067978 Simplifying x = -0.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.236067978, -0.236067978}

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