5(x+7)+3=34x(x-4)

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Solution for 5(x+7)+3=34x(x-4) equation:


Simplifying
5(x + 7) + 3 = 34x(x + -4)

Reorder the terms:
5(7 + x) + 3 = 34x(x + -4)
(7 * 5 + x * 5) + 3 = 34x(x + -4)
(35 + 5x) + 3 = 34x(x + -4)

Reorder the terms:
35 + 3 + 5x = 34x(x + -4)

Combine like terms: 35 + 3 = 38
38 + 5x = 34x(x + -4)

Reorder the terms:
38 + 5x = 34x(-4 + x)
38 + 5x = (-4 * 34x + x * 34x)
38 + 5x = (-136x + 34x2)

Solving
38 + 5x = -136x + 34x2

Solving for variable 'x'.

Combine like terms: 5x + 136x = 141x
38 + 141x + -34x2 = -136x + 34x2 + 136x + -34x2

Reorder the terms:
38 + 141x + -34x2 = -136x + 136x + 34x2 + -34x2

Combine like terms: -136x + 136x = 0
38 + 141x + -34x2 = 0 + 34x2 + -34x2
38 + 141x + -34x2 = 34x2 + -34x2

Combine like terms: 34x2 + -34x2 = 0
38 + 141x + -34x2 = 0

Begin completing the square.  Divide all terms by
-34 the coefficient of the squared term: 

Divide each side by '-34'.
-1.117647059 + -4.147058824x + x2 = 0

Move the constant term to the right:

Add '1.117647059' to each side of the equation.
-1.117647059 + -4.147058824x + 1.117647059 + x2 = 0 + 1.117647059

Reorder the terms:
-1.117647059 + 1.117647059 + -4.147058824x + x2 = 0 + 1.117647059

Combine like terms: -1.117647059 + 1.117647059 = 0.000000000
0.000000000 + -4.147058824x + x2 = 0 + 1.117647059
-4.147058824x + x2 = 0 + 1.117647059

Combine like terms: 0 + 1.117647059 = 1.117647059
-4.147058824x + x2 = 1.117647059

The x term is -4.147058824x.  Take half its coefficient (-2.073529412).
Square it (4.299524222) and add it to both sides.

Add '4.299524222' to each side of the equation.
-4.147058824x + 4.299524222 + x2 = 1.117647059 + 4.299524222

Reorder the terms:
4.299524222 + -4.147058824x + x2 = 1.117647059 + 4.299524222

Combine like terms: 1.117647059 + 4.299524222 = 5.417171281
4.299524222 + -4.147058824x + x2 = 5.417171281

Factor a perfect square on the left side:
(x + -2.073529412)(x + -2.073529412) = 5.417171281

Calculate the square root of the right side: 2.327481747

Break this problem into two subproblems by setting 
(x + -2.073529412) equal to 2.327481747 and -2.327481747.

Subproblem 1

x + -2.073529412 = 2.327481747 Simplifying x + -2.073529412 = 2.327481747 Reorder the terms: -2.073529412 + x = 2.327481747 Solving -2.073529412 + x = 2.327481747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.073529412' to each side of the equation. -2.073529412 + 2.073529412 + x = 2.327481747 + 2.073529412 Combine like terms: -2.073529412 + 2.073529412 = 0.000000000 0.000000000 + x = 2.327481747 + 2.073529412 x = 2.327481747 + 2.073529412 Combine like terms: 2.327481747 + 2.073529412 = 4.401011159 x = 4.401011159 Simplifying x = 4.401011159

Subproblem 2

x + -2.073529412 = -2.327481747 Simplifying x + -2.073529412 = -2.327481747 Reorder the terms: -2.073529412 + x = -2.327481747 Solving -2.073529412 + x = -2.327481747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.073529412' to each side of the equation. -2.073529412 + 2.073529412 + x = -2.327481747 + 2.073529412 Combine like terms: -2.073529412 + 2.073529412 = 0.000000000 0.000000000 + x = -2.327481747 + 2.073529412 x = -2.327481747 + 2.073529412 Combine like terms: -2.327481747 + 2.073529412 = -0.253952335 x = -0.253952335 Simplifying x = -0.253952335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.401011159, -0.253952335}

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