(4x^2-9x+1)+(x^2-5x-3)=

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Solution for (4x^2-9x+1)+(x^2-5x-3)= equation:


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

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

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

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

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

Reorder the terms:
1 + -3 + -9x + -5x + 4x2 + x2 = 0

Combine like terms: 1 + -3 = -2
-2 + -9x + -5x + 4x2 + x2 = 0

Combine like terms: -9x + -5x = -14x
-2 + -14x + 4x2 + x2 = 0

Combine like terms: 4x2 + x2 = 5x2
-2 + -14x + 5x2 = 0

Solving
-2 + -14x + 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'.
-0.4 + -2.8x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -2.8x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -2.8x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -2.8x + x2 = 0 + 0.4
-2.8x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-2.8x + x2 = 0.4

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = 0.4 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 0.4 + 1.96

Combine like terms: 0.4 + 1.96 = 2.36
1.96 + -2.8x + x2 = 2.36

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 2.36

Calculate the square root of the right side: 1.53622915

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.53622915 and -1.53622915.

Subproblem 1

x + -1.4 = 1.53622915 Simplifying x + -1.4 = 1.53622915 Reorder the terms: -1.4 + x = 1.53622915 Solving -1.4 + x = 1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.53622915 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.53622915 + 1.4 x = 1.53622915 + 1.4 Combine like terms: 1.53622915 + 1.4 = 2.93622915 x = 2.93622915 Simplifying x = 2.93622915

Subproblem 2

x + -1.4 = -1.53622915 Simplifying x + -1.4 = -1.53622915 Reorder the terms: -1.4 + x = -1.53622915 Solving -1.4 + x = -1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.53622915 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.53622915 + 1.4 x = -1.53622915 + 1.4 Combine like terms: -1.53622915 + 1.4 = -0.13622915 x = -0.13622915 Simplifying x = -0.13622915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.93622915, -0.13622915}

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