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

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


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

Reorder the terms:
7x2 + -5x + 4(4 + -9x) = 0
7x2 + -5x + (4 * 4 + -9x * 4) = 0
7x2 + -5x + (16 + -36x) = 0

Reorder the terms:
16 + -5x + -36x + 7x2 = 0

Combine like terms: -5x + -36x = -41x
16 + -41x + 7x2 = 0

Solving
16 + -41x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
2.285714286 + -5.857142857x + x2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + -5.857142857x + -2.285714286 + x2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + -5.857142857x + x2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + -5.857142857x + x2 = 0 + -2.285714286
-5.857142857x + x2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
-5.857142857x + x2 = -2.285714286

The x term is -5.857142857x.  Take half its coefficient (-2.928571429).
Square it (8.576530615) and add it to both sides.

Add '8.576530615' to each side of the equation.
-5.857142857x + 8.576530615 + x2 = -2.285714286 + 8.576530615

Reorder the terms:
8.576530615 + -5.857142857x + x2 = -2.285714286 + 8.576530615

Combine like terms: -2.285714286 + 8.576530615 = 6.290816329
8.576530615 + -5.857142857x + x2 = 6.290816329

Factor a perfect square on the left side:
(x + -2.928571429)(x + -2.928571429) = 6.290816329

Calculate the square root of the right side: 2.508149981

Break this problem into two subproblems by setting 
(x + -2.928571429) equal to 2.508149981 and -2.508149981.

Subproblem 1

x + -2.928571429 = 2.508149981 Simplifying x + -2.928571429 = 2.508149981 Reorder the terms: -2.928571429 + x = 2.508149981 Solving -2.928571429 + x = 2.508149981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + x = 2.508149981 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + x = 2.508149981 + 2.928571429 x = 2.508149981 + 2.928571429 Combine like terms: 2.508149981 + 2.928571429 = 5.43672141 x = 5.43672141 Simplifying x = 5.43672141

Subproblem 2

x + -2.928571429 = -2.508149981 Simplifying x + -2.928571429 = -2.508149981 Reorder the terms: -2.928571429 + x = -2.508149981 Solving -2.928571429 + x = -2.508149981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + x = -2.508149981 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + x = -2.508149981 + 2.928571429 x = -2.508149981 + 2.928571429 Combine like terms: -2.508149981 + 2.928571429 = 0.420421448 x = 0.420421448 Simplifying x = 0.420421448

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.43672141, 0.420421448}

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