0=2(x+5)(x-3)+35

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Solution for 0=2(x+5)(x-3)+35 equation:


Simplifying
0 = 2(x + 5)(x + -3) + 35

Reorder the terms:
0 = 2(5 + x)(x + -3) + 35

Reorder the terms:
0 = 2(5 + x)(-3 + x) + 35

Multiply (5 + x) * (-3 + x)
0 = 2(5(-3 + x) + x(-3 + x)) + 35
0 = 2((-3 * 5 + x * 5) + x(-3 + x)) + 35
0 = 2((-15 + 5x) + x(-3 + x)) + 35
0 = 2(-15 + 5x + (-3 * x + x * x)) + 35
0 = 2(-15 + 5x + (-3x + x2)) + 35

Combine like terms: 5x + -3x = 2x
0 = 2(-15 + 2x + x2) + 35
0 = (-15 * 2 + 2x * 2 + x2 * 2) + 35
0 = (-30 + 4x + 2x2) + 35

Reorder the terms:
0 = -30 + 35 + 4x + 2x2

Combine like terms: -30 + 35 = 5
0 = 5 + 4x + 2x2

Solving
0 = 5 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -4x + -2x2 = 5 + 4x + 2x2 + -5 + -4x + -2x2

Reorder the terms:
-5 + -4x + -2x2 = 5 + -5 + 4x + -4x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-5 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
-5 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
-5 + -4x + -2x2 = 0 + 2x2 + -2x2
-5 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 4x + 2x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x + 2x2 = 0

Solving
5 + 4x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 2x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 2x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 2x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 2x + x2 = 0 + -2.5
2x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
2x + x2 = -2.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -2.5 + 1

Reorder the terms:
1 + 2x + x2 = -2.5 + 1

Combine like terms: -2.5 + 1 = -1.5
1 + 2x + x2 = -1.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -1.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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