0=4x^2+26x-14

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Solution for 0=4x^2+26x-14 equation:


Simplifying
0 = 4x2 + 26x + -14

Reorder the terms:
0 = -14 + 26x + 4x2

Solving
0 = -14 + 26x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + -26x + -4x2 = -14 + 26x + 4x2 + 14 + -26x + -4x2

Reorder the terms:
14 + -26x + -4x2 = -14 + 14 + 26x + -26x + 4x2 + -4x2

Combine like terms: -14 + 14 = 0
14 + -26x + -4x2 = 0 + 26x + -26x + 4x2 + -4x2
14 + -26x + -4x2 = 26x + -26x + 4x2 + -4x2

Combine like terms: 26x + -26x = 0
14 + -26x + -4x2 = 0 + 4x2 + -4x2
14 + -26x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
14 + -26x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -13x + -2x2) = 0

Factor a trinomial.
2((1 + -2x)(7 + x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0.5, -7}

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