(4x^2+7x-15)-(2x^2+2x-4)=0

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Solution for (4x^2+7x-15)-(2x^2+2x-4)=0 equation:


Simplifying
(4x2 + 7x + -15) + -1(2x2 + 2x + -4) = 0

Reorder the terms:
(-15 + 7x + 4x2) + -1(2x2 + 2x + -4) = 0

Remove parenthesis around (-15 + 7x + 4x2)
-15 + 7x + 4x2 + -1(2x2 + 2x + -4) = 0

Reorder the terms:
-15 + 7x + 4x2 + -1(-4 + 2x + 2x2) = 0
-15 + 7x + 4x2 + (-4 * -1 + 2x * -1 + 2x2 * -1) = 0
-15 + 7x + 4x2 + (4 + -2x + -2x2) = 0

Reorder the terms:
-15 + 4 + 7x + -2x + 4x2 + -2x2 = 0

Combine like terms: -15 + 4 = -11
-11 + 7x + -2x + 4x2 + -2x2 = 0

Combine like terms: 7x + -2x = 5x
-11 + 5x + 4x2 + -2x2 = 0

Combine like terms: 4x2 + -2x2 = 2x2
-11 + 5x + 2x2 = 0

Solving
-11 + 5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-5.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 2.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 2.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 2.5x + x2 = 0 + 5.5
2.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
2.5x + x2 = 5.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 5.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 5.5 + 1.5625

Combine like terms: 5.5 + 1.5625 = 7.0625
1.5625 + 2.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

x + 1.25 = 2.657536453 Simplifying x + 1.25 = 2.657536453 Reorder the terms: 1.25 + x = 2.657536453 Solving 1.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.657536453 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.657536453 + -1.25 x = 2.657536453 + -1.25 Combine like terms: 2.657536453 + -1.25 = 1.407536453 x = 1.407536453 Simplifying x = 1.407536453

Subproblem 2

x + 1.25 = -2.657536453 Simplifying x + 1.25 = -2.657536453 Reorder the terms: 1.25 + x = -2.657536453 Solving 1.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.657536453 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.657536453 + -1.25 x = -2.657536453 + -1.25 Combine like terms: -2.657536453 + -1.25 = -3.907536453 x = -3.907536453 Simplifying x = -3.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.407536453, -3.907536453}

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