(4x^2)+(10x)=x^2-x+4

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Solution for (4x^2)+(10x)=x^2-x+4 equation:


Simplifying
(4x2) + (10x) = x2 + -1x + 4

Reorder the terms:
(10x) + (4x2) = x2 + -1x + 4

Reorder the terms:
(10x) + (4x2) = 4 + -1x + x2

Solving
(10x) + (4x2) = 4 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + (10x) + x + (4x2) + -1x2 = 4 + -1x + x2 + -4 + x + -1x2

Combine like terms: (10x) + x = 11x
-4 + 11x + (4x2) + -1x2 = 4 + -1x + x2 + -4 + x + -1x2

Combine like terms: (4x2) + -1x2 = 3x2
-4 + 11x + 3x2 = 4 + -1x + x2 + -4 + x + -1x2

Reorder the terms:
-4 + 11x + 3x2 = 4 + -4 + -1x + x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + 11x + 3x2 = 0 + -1x + x + x2 + -1x2
-4 + 11x + 3x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-4 + 11x + 3x2 = 0 + x2 + -1x2
-4 + 11x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 11x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -3x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {-4, 0.3333333333}

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