7x^2+11x=4

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Solution for 7x^2+11x=4 equation:


Simplifying
7x2 + 11x = 4

Reorder the terms:
11x + 7x2 = 4

Solving
11x + 7x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 11x + 7x2 = 4 + -4

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

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

Divide each side by '7'.
-0.5714285714 + 1.571428571x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 1.571428571x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 1.571428571x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 1.571428571x + x2 = 0 + 0.5714285714
1.571428571x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
1.571428571x + x2 = 0.5714285714

The x term is 1.571428571x.  Take half its coefficient (0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
1.571428571x + 0.6173469384 + x2 = 0.5714285714 + 0.6173469384

Reorder the terms:
0.6173469384 + 1.571428571x + x2 = 0.5714285714 + 0.6173469384

Combine like terms: 0.5714285714 + 0.6173469384 = 1.1887755098
0.6173469384 + 1.571428571x + x2 = 1.1887755098

Factor a perfect square on the left side:
(x + 0.7857142855)(x + 0.7857142855) = 1.1887755098

Calculate the square root of the right side: 1.090309823

Break this problem into two subproblems by setting 
(x + 0.7857142855) equal to 1.090309823 and -1.090309823.

Subproblem 1

x + 0.7857142855 = 1.090309823 Simplifying x + 0.7857142855 = 1.090309823 Reorder the terms: 0.7857142855 + x = 1.090309823 Solving 0.7857142855 + x = 1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 1.090309823 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 1.090309823 + -0.7857142855 x = 1.090309823 + -0.7857142855 Combine like terms: 1.090309823 + -0.7857142855 = 0.3045955375 x = 0.3045955375 Simplifying x = 0.3045955375

Subproblem 2

x + 0.7857142855 = -1.090309823 Simplifying x + 0.7857142855 = -1.090309823 Reorder the terms: 0.7857142855 + x = -1.090309823 Solving 0.7857142855 + x = -1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -1.090309823 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -1.090309823 + -0.7857142855 x = -1.090309823 + -0.7857142855 Combine like terms: -1.090309823 + -0.7857142855 = -1.8760241085 x = -1.8760241085 Simplifying x = -1.8760241085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3045955375, -1.8760241085}

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