x*x+7x-11=6x+1

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Solution for x*x+7x-11=6x+1 equation:


Simplifying
x * x + 7x + -11 = 6x + 1

Multiply x * x
x2 + 7x + -11 = 6x + 1

Reorder the terms:
-11 + 7x + x2 = 6x + 1

Reorder the terms:
-11 + 7x + x2 = 1 + 6x

Solving
-11 + 7x + x2 = 1 + 6x

Solving for variable 'x'.

Reorder the terms:
-11 + -1 + 7x + -6x + x2 = 1 + 6x + -1 + -6x

Combine like terms: -11 + -1 = -12
-12 + 7x + -6x + x2 = 1 + 6x + -1 + -6x

Combine like terms: 7x + -6x = 1x
-12 + 1x + x2 = 1 + 6x + -1 + -6x

Reorder the terms:
-12 + 1x + x2 = 1 + -1 + 6x + -6x

Combine like terms: 1 + -1 = 0
-12 + 1x + x2 = 0 + 6x + -6x
-12 + 1x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-4, 3}

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