(2x-7)(x+3)=4

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Solution for (2x-7)(x+3)=4 equation:


Simplifying
(2x + -7)(x + 3) = 4

Reorder the terms:
(-7 + 2x)(x + 3) = 4

Reorder the terms:
(-7 + 2x)(3 + x) = 4

Multiply (-7 + 2x) * (3 + x)
(-7(3 + x) + 2x * (3 + x)) = 4
((3 * -7 + x * -7) + 2x * (3 + x)) = 4
((-21 + -7x) + 2x * (3 + x)) = 4
(-21 + -7x + (3 * 2x + x * 2x)) = 4
(-21 + -7x + (6x + 2x2)) = 4

Combine like terms: -7x + 6x = -1x
(-21 + -1x + 2x2) = 4

Solving
-21 + -1x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-21 + -4 + -1x + 2x2 = 4 + -4

Combine like terms: -21 + -4 = -25
-25 + -1x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-25 + -1x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -0.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -0.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -0.5x + x2 = 0 + 12.5
-0.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-0.5x + x2 = 12.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 12.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 12.5 + 0.0625

Combine like terms: 12.5 + 0.0625 = 12.5625
0.0625 + -0.5x + x2 = 12.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.54436172 and -3.54436172.

Subproblem 1

x + -0.25 = 3.54436172 Simplifying x + -0.25 = 3.54436172 Reorder the terms: -0.25 + x = 3.54436172 Solving -0.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.54436172 + 0.25 x = 3.54436172 + 0.25 Combine like terms: 3.54436172 + 0.25 = 3.79436172 x = 3.79436172 Simplifying x = 3.79436172

Subproblem 2

x + -0.25 = -3.54436172 Simplifying x + -0.25 = -3.54436172 Reorder the terms: -0.25 + x = -3.54436172 Solving -0.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.54436172 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.54436172 + 0.25 x = -3.54436172 + 0.25 Combine like terms: -3.54436172 + 0.25 = -3.29436172 x = -3.29436172 Simplifying x = -3.29436172

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.79436172, -3.29436172}

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