0=18a^2-5a-7

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Solution for 0=18a^2-5a-7 equation:


Simplifying
0 = 18a2 + -5a + -7

Reorder the terms:
0 = -7 + -5a + 18a2

Solving
0 = -7 + -5a + 18a2

Solving for variable 'a'.

Combine like terms: 0 + 7 = 7
7 + 5a + -18a2 = -7 + -5a + 18a2 + 7 + 5a + -18a2

Reorder the terms:
7 + 5a + -18a2 = -7 + 7 + -5a + 5a + 18a2 + -18a2

Combine like terms: -7 + 7 = 0
7 + 5a + -18a2 = 0 + -5a + 5a + 18a2 + -18a2
7 + 5a + -18a2 = -5a + 5a + 18a2 + -18a2

Combine like terms: -5a + 5a = 0
7 + 5a + -18a2 = 0 + 18a2 + -18a2
7 + 5a + -18a2 = 18a2 + -18a2

Combine like terms: 18a2 + -18a2 = 0
7 + 5a + -18a2 = 0

Factor a trinomial.
(7 + -9a)(1 + 2a) = 0

Subproblem 1

Set the factor '(7 + -9a)' equal to zero and attempt to solve: Simplifying 7 + -9a = 0 Solving 7 + -9a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9a = 0 + -7 -9a = 0 + -7 Combine like terms: 0 + -7 = -7 -9a = -7 Divide each side by '-9'. a = 0.7777777778 Simplifying a = 0.7777777778

Subproblem 2

Set the factor '(1 + 2a)' equal to zero and attempt to solve: Simplifying 1 + 2a = 0 Solving 1 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2a = 0 + -1 2a = 0 + -1 Combine like terms: 0 + -1 = -1 2a = -1 Divide each side by '2'. a = -0.5 Simplifying a = -0.5

Solution

a = {0.7777777778, -0.5}

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