0=8x^2-30x-50

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Solution for 0=8x^2-30x-50 equation:


Simplifying
0 = 8x2 + -30x + -50

Reorder the terms:
0 = -50 + -30x + 8x2

Solving
0 = -50 + -30x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 50 = 50
50 + 30x + -8x2 = -50 + -30x + 8x2 + 50 + 30x + -8x2

Reorder the terms:
50 + 30x + -8x2 = -50 + 50 + -30x + 30x + 8x2 + -8x2

Combine like terms: -50 + 50 = 0
50 + 30x + -8x2 = 0 + -30x + 30x + 8x2 + -8x2
50 + 30x + -8x2 = -30x + 30x + 8x2 + -8x2

Combine like terms: -30x + 30x = 0
50 + 30x + -8x2 = 0 + 8x2 + -8x2
50 + 30x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
50 + 30x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 15x + -4x2) = 0

Factor a trinomial.
2((5 + -1x)(5 + 4x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25

Solution

x = {5, -1.25}

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