(2x+3)(x-3)=25

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Solution for (2x+3)(x-3)=25 equation:


Simplifying
(2x + 3)(x + -3) = 25

Reorder the terms:
(3 + 2x)(x + -3) = 25

Reorder the terms:
(3 + 2x)(-3 + x) = 25

Multiply (3 + 2x) * (-3 + x)
(3(-3 + x) + 2x * (-3 + x)) = 25
((-3 * 3 + x * 3) + 2x * (-3 + x)) = 25
((-9 + 3x) + 2x * (-3 + x)) = 25
(-9 + 3x + (-3 * 2x + x * 2x)) = 25
(-9 + 3x + (-6x + 2x2)) = 25

Combine like terms: 3x + -6x = -3x
(-9 + -3x + 2x2) = 25

Solving
-9 + -3x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
-9 + -25 + -3x + 2x2 = 25 + -25

Combine like terms: -9 + -25 = -34
-34 + -3x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-34 + -3x + 2x2 = 0

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

Divide each side by '2'.
-17 + -1.5x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -1.5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -1.5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1.5x + x2 = 0 + 17
-1.5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-1.5x + x2 = 17

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 17 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 17 + 0.5625

Combine like terms: 17 + 0.5625 = 17.5625
0.5625 + -1.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -0.75) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + -0.75 = 4.190763654 Simplifying x + -0.75 = 4.190763654 Reorder the terms: -0.75 + x = 4.190763654 Solving -0.75 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 4.190763654 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.190763654 + 0.75 x = 4.190763654 + 0.75 Combine like terms: 4.190763654 + 0.75 = 4.940763654 x = 4.940763654 Simplifying x = 4.940763654

Subproblem 2

x + -0.75 = -4.190763654 Simplifying x + -0.75 = -4.190763654 Reorder the terms: -0.75 + x = -4.190763654 Solving -0.75 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -4.190763654 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.190763654 + 0.75 x = -4.190763654 + 0.75 Combine like terms: -4.190763654 + 0.75 = -3.440763654 x = -3.440763654 Simplifying x = -3.440763654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.940763654, -3.440763654}

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