0=14x^2-9x+1

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Solution for 0=14x^2-9x+1 equation:


Simplifying
0 = 14x2 + -9x + 1

Reorder the terms:
0 = 1 + -9x + 14x2

Solving
0 = 1 + -9x + 14x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 9x + -14x2 = 1 + -9x + 14x2 + -1 + 9x + -14x2

Reorder the terms:
-1 + 9x + -14x2 = 1 + -1 + -9x + 9x + 14x2 + -14x2

Combine like terms: 1 + -1 = 0
-1 + 9x + -14x2 = 0 + -9x + 9x + 14x2 + -14x2
-1 + 9x + -14x2 = -9x + 9x + 14x2 + -14x2

Combine like terms: -9x + 9x = 0
-1 + 9x + -14x2 = 0 + 14x2 + -14x2
-1 + 9x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
-1 + 9x + -14x2 = 0

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

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 '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429

Solution

x = {0.5, 0.1428571429}

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