(2x+10)(x-4)=21

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Solution for (2x+10)(x-4)=21 equation:


Simplifying
(2x + 10)(x + -4) = 21

Reorder the terms:
(10 + 2x)(x + -4) = 21

Reorder the terms:
(10 + 2x)(-4 + x) = 21

Multiply (10 + 2x) * (-4 + x)
(10(-4 + x) + 2x * (-4 + x)) = 21
((-4 * 10 + x * 10) + 2x * (-4 + x)) = 21
((-40 + 10x) + 2x * (-4 + x)) = 21
(-40 + 10x + (-4 * 2x + x * 2x)) = 21
(-40 + 10x + (-8x + 2x2)) = 21

Combine like terms: 10x + -8x = 2x
(-40 + 2x + 2x2) = 21

Solving
-40 + 2x + 2x2 = 21

Solving for variable 'x'.

Reorder the terms:
-40 + -21 + 2x + 2x2 = 21 + -21

Combine like terms: -40 + -21 = -61
-61 + 2x + 2x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-61 + 2x + 2x2 = 0

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

Divide each side by '2'.
-30.5 + x + x2 = 0

Move the constant term to the right:

Add '30.5' to each side of the equation.
-30.5 + x + 30.5 + x2 = 0 + 30.5

Reorder the terms:
-30.5 + 30.5 + x + x2 = 0 + 30.5

Combine like terms: -30.5 + 30.5 = 0.0
0.0 + x + x2 = 0 + 30.5
x + x2 = 0 + 30.5

Combine like terms: 0 + 30.5 = 30.5
x + x2 = 30.5

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 30.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 30.5 + 0.25

Combine like terms: 30.5 + 0.25 = 30.75
1.25 + x2 = 30.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 30.75

Calculate the square root of the right side: 5.545268253

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.545268253 and -5.545268253.

Subproblem 1

x + 0.5 = 5.545268253 Simplifying x + 0.5 = 5.545268253 Reorder the terms: 0.5 + x = 5.545268253 Solving 0.5 + x = 5.545268253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.545268253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.545268253 + -0.5 x = 5.545268253 + -0.5 Combine like terms: 5.545268253 + -0.5 = 5.045268253 x = 5.045268253 Simplifying x = 5.045268253

Subproblem 2

x + 0.5 = -5.545268253 Simplifying x + 0.5 = -5.545268253 Reorder the terms: 0.5 + x = -5.545268253 Solving 0.5 + x = -5.545268253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.545268253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.545268253 + -0.5 x = -5.545268253 + -0.5 Combine like terms: -5.545268253 + -0.5 = -6.045268253 x = -6.045268253 Simplifying x = -6.045268253

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.045268253, -6.045268253}

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