0=2x^2+7x+5

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Solution for 0=2x^2+7x+5 equation:


Simplifying
0 = 2x2 + 7x + 5

Reorder the terms:
0 = 5 + 7x + 2x2

Solving
0 = 5 + 7x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -7x + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Reorder the terms:
-5 + -7x + -2x2 = 5 + -5 + 7x + -7x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-5 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2
-5 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-5 + -7x + -2x2 = 0 + 2x2 + -2x2
-5 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + -7x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 7x + 2x2) = 0

Factor a trinomial.
-1((5 + 2x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-2.5, -1}

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