5x^2+11x=7(x+3)

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Solution for 5x^2+11x=7(x+3) equation:


Simplifying
5x2 + 11x = 7(x + 3)

Reorder the terms:
11x + 5x2 = 7(x + 3)

Reorder the terms:
11x + 5x2 = 7(3 + x)
11x + 5x2 = (3 * 7 + x * 7)
11x + 5x2 = (21 + 7x)

Solving
11x + 5x2 = 21 + 7x

Solving for variable 'x'.

Reorder the terms:
-21 + 11x + -7x + 5x2 = 21 + 7x + -21 + -7x

Combine like terms: 11x + -7x = 4x
-21 + 4x + 5x2 = 21 + 7x + -21 + -7x

Reorder the terms:
-21 + 4x + 5x2 = 21 + -21 + 7x + -7x

Combine like terms: 21 + -21 = 0
-21 + 4x + 5x2 = 0 + 7x + -7x
-21 + 4x + 5x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-21 + 4x + 5x2 = 0

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

Divide each side by '5'.
-4.2 + 0.8x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + 0.8x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + 0.8x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + 0.8x + x2 = 0 + 4.2
0.8x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
0.8x + x2 = 4.2

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 4.2 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 4.2 + 0.16

Combine like terms: 4.2 + 0.16 = 4.36
0.16 + 0.8x + x2 = 4.36

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 4.36

Calculate the square root of the right side: 2.088061302

Break this problem into two subproblems by setting 
(x + 0.4) equal to 2.088061302 and -2.088061302.

Subproblem 1

x + 0.4 = 2.088061302 Simplifying x + 0.4 = 2.088061302 Reorder the terms: 0.4 + x = 2.088061302 Solving 0.4 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.088061302 + -0.4 x = 2.088061302 + -0.4 Combine like terms: 2.088061302 + -0.4 = 1.688061302 x = 1.688061302 Simplifying x = 1.688061302

Subproblem 2

x + 0.4 = -2.088061302 Simplifying x + 0.4 = -2.088061302 Reorder the terms: 0.4 + x = -2.088061302 Solving 0.4 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.088061302 + -0.4 x = -2.088061302 + -0.4 Combine like terms: -2.088061302 + -0.4 = -2.488061302 x = -2.488061302 Simplifying x = -2.488061302

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.688061302, -2.488061302}

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