(2x+9)(x-5)=50

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Solution for (2x+9)(x-5)=50 equation:


Simplifying
(2x + 9)(x + -5) = 50

Reorder the terms:
(9 + 2x)(x + -5) = 50

Reorder the terms:
(9 + 2x)(-5 + x) = 50

Multiply (9 + 2x) * (-5 + x)
(9(-5 + x) + 2x * (-5 + x)) = 50
((-5 * 9 + x * 9) + 2x * (-5 + x)) = 50
((-45 + 9x) + 2x * (-5 + x)) = 50
(-45 + 9x + (-5 * 2x + x * 2x)) = 50
(-45 + 9x + (-10x + 2x2)) = 50

Combine like terms: 9x + -10x = -1x
(-45 + -1x + 2x2) = 50

Solving
-45 + -1x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
-45 + -50 + -1x + 2x2 = 50 + -50

Combine like terms: -45 + -50 = -95
-95 + -1x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-95 + -1x + 2x2 = 0

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

Divide each side by '2'.
-47.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '47.5' to each side of the equation.
-47.5 + -0.5x + 47.5 + x2 = 0 + 47.5

Reorder the terms:
-47.5 + 47.5 + -0.5x + x2 = 0 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + -0.5x + x2 = 0 + 47.5
-0.5x + x2 = 0 + 47.5

Combine like terms: 0 + 47.5 = 47.5
-0.5x + x2 = 47.5

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 = 47.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 47.5 + 0.0625

Combine like terms: 47.5 + 0.0625 = 47.5625
0.0625 + -0.5x + x2 = 47.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 47.5625

Calculate the square root of the right side: 6.896557112

Break this problem into two subproblems by setting 
(x + -0.25) equal to 6.896557112 and -6.896557112.

Subproblem 1

x + -0.25 = 6.896557112 Simplifying x + -0.25 = 6.896557112 Reorder the terms: -0.25 + x = 6.896557112 Solving -0.25 + x = 6.896557112 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 = 6.896557112 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.896557112 + 0.25 x = 6.896557112 + 0.25 Combine like terms: 6.896557112 + 0.25 = 7.146557112 x = 7.146557112 Simplifying x = 7.146557112

Subproblem 2

x + -0.25 = -6.896557112 Simplifying x + -0.25 = -6.896557112 Reorder the terms: -0.25 + x = -6.896557112 Solving -0.25 + x = -6.896557112 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 = -6.896557112 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.896557112 + 0.25 x = -6.896557112 + 0.25 Combine like terms: -6.896557112 + 0.25 = -6.646557112 x = -6.646557112 Simplifying x = -6.646557112

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.146557112, -6.646557112}

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