7x^2+5=4x+6

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Solution for 7x^2+5=4x+6 equation:


Simplifying
7x2 + 5 = 4x + 6

Reorder the terms:
5 + 7x2 = 4x + 6

Reorder the terms:
5 + 7x2 = 6 + 4x

Solving
5 + 7x2 = 6 + 4x

Solving for variable 'x'.

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

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

Reorder the terms:
-1 + -4x + 7x2 = 6 + -6 + 4x + -4x

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

Combine like terms: 4x + -4x = 0
-1 + -4x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + -0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -0.5714285714x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -0.5714285714x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -0.5714285714x + x2 = 0 + 0.1428571429
-0.5714285714x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-0.5714285714x + x2 = 0.1428571429

The x term is -0.5714285714x.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714x + 0.08163265305 + x2 = 0.1428571429 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714x + x2 = 0.1428571429 + 0.08163265305

Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595
0.08163265305 + -0.5714285714x + x2 = 0.22448979595

Factor a perfect square on the left side:
(x + -0.2857142857)(x + -0.2857142857) = 0.22448979595

Calculate the square root of the right side: 0.473803542

Break this problem into two subproblems by setting 
(x + -0.2857142857) equal to 0.473803542 and -0.473803542.

Subproblem 1

x + -0.2857142857 = 0.473803542 Simplifying x + -0.2857142857 = 0.473803542 Reorder the terms: -0.2857142857 + x = 0.473803542 Solving -0.2857142857 + x = 0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.473803542 + 0.2857142857 x = 0.473803542 + 0.2857142857 Combine like terms: 0.473803542 + 0.2857142857 = 0.7595178277 x = 0.7595178277 Simplifying x = 0.7595178277

Subproblem 2

x + -0.2857142857 = -0.473803542 Simplifying x + -0.2857142857 = -0.473803542 Reorder the terms: -0.2857142857 + x = -0.473803542 Solving -0.2857142857 + x = -0.473803542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.473803542 + 0.2857142857 x = -0.473803542 + 0.2857142857 Combine like terms: -0.473803542 + 0.2857142857 = -0.1880892563 x = -0.1880892563 Simplifying x = -0.1880892563

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7595178277, -0.1880892563}

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