6=7x+xwhere x≠0 7x=6−x x2⋅7x=x2(6−x) 7x=6x2−x3 x3−6x2+7x=0 x(x2−6x+7)=0 x=0or x2−6x+7=0 For x2−6x+7=0, we need to use the quadratic formula i.e. x=−b±b2−4ac2a x=6±36−282 x=6±222 x=3±2 But looking at x=0, it cannot be a solution because of 70 Answer: x=3±2

Get the solution to "What is x if 6=7x+x?"

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

Jessica Collier

Answered question

2022-02-04

What is x if

6 = \frac{7}{x} + x

Answer & Explanation

iloverayyeb

Beginner2022-02-05Added 14 answers

6 = \frac{7}{x} + x where x \neq 0

\frac{7}{x} = 6 - x

x^{2} \cdot \frac{7}{x} = x^{2} (6 - x)

7 x = 6 x^{2} - x^{3}

x^{3} - 6 x^{2} + 7 x = 0

x (x^{2} - 6 x + 7) = 0

x = 0 or x^{2} - 6 x + 7 = 0

For

x^{2} - 6 x + 7 = 0

, we need to use the quadratic formula
i.e.

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

x = \frac{6 \pm \sqrt{36 - 28}}{2}

x = \frac{6 \pm 2 \sqrt{2}}{2}

x = 3 \pm \sqrt{2}

But looking at

x = 0

, it cannot be a solution because of

\frac{7}{0}

Answer:

x = 3 \pm \sqrt{2}

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