Expert Answer to "What is x if 2x−3x=11?"

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

scrimaeua

Answered question

2022-02-04

What is x if

2 x - \frac{3}{x} = 11

Answer & Explanation

mikedejoyacqs

Beginner2022-02-05Added 11 answers

Step 1
$2 x - \frac{3}{x} = 11$
Multiply both sides by the LCD x.
$2 x (x) - \frac{3}{⧸ x} (⧸ x) = 11 (x) =$
$2 x^{2} - 3 = 11 x$
Step 2
Move all terms to the left side.
$2 x^{2} - 3 - 11 x = 0$
Rearrange the terms.
$2 x^{2} - 11 x - 3$
Step 3
Apply the quadratic formula.
$2 x^{2} - 11 x - 3$ is in the form of a quadratic equation $a x + b x + c$ , where $a = 2, b = - 11, and c = - 3$ .
Quadratic Formula
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} =$
$x = \frac{- (- 11) \pm \sqrt{(- 11^{2}) - (4 \cdot 2 \cdot - 3)}}{2 \cdot 2} =$
$x = \frac{11 \pm \sqrt{121 + 24}}{4} =$
$x = \frac{11 \pm \sqrt{145}}{4}$
Solve for x.
$x = \frac{11 + \sqrt{145}}{4}, \frac{11 - \sqrt{145}}{4}$

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