5x^2=19x+4

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Solution for 5x^2=19x+4 equation:


Simplifying
5x2 = 19x + 4

Reorder the terms:
5x2 = 4 + 19x

Solving
5x2 = 4 + 19x

Solving for variable 'x'.

Reorder the terms:
-4 + -19x + 5x2 = 4 + 19x + -4 + -19x

Reorder the terms:
-4 + -19x + 5x2 = 4 + -4 + 19x + -19x

Combine like terms: 4 + -4 = 0
-4 + -19x + 5x2 = 0 + 19x + -19x
-4 + -19x + 5x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
-4 + -19x + 5x2 = 0

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

Subproblem 1

Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-0.2, 4}

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