x(4x-7)=11

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Solution for x(4x-7)=11 equation:


Simplifying
x(4x + -7) = 11

Reorder the terms:
x(-7 + 4x) = 11
(-7 * x + 4x * x) = 11
(-7x + 4x2) = 11

Solving
-7x + 4x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + -7x + 4x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -7x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(11 + -4x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(11 + -4x)' equal to zero and attempt to solve: Simplifying 11 + -4x = 0 Solving 11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4x = 0 + -11 -4x = 0 + -11 Combine like terms: 0 + -11 = -11 -4x = -11 Divide each side by '-4'. x = 2.75 Simplifying x = 2.75

Solution

x = {-1, 2.75}

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