Solve 2x^212x=7x 7

Question

Solve the equation

x_{1} = - \frac{7 6}{12}, x_{2} = 0, x_{3} = \frac{7 6}{12}

Alternative Form

x_{1} \approx - 1.428869, x_{2} = 0, x_{3} \approx 1.428869

Evaluate

2 x^{2} \times 12 x = 7 x \times 7

Multiply

More Steps

Evaluate

2 x^{2} \times 12 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} = 7 x \times 7

Multiply the terms

24 x^{3} = 49 x

Add or subtract both sides

24 x^{3} - 49 x = 0

Factor the expression

x (24 x^{2} - 49) = 0

Separate the equation into 2 possible cases

x = 0 24 x^{2} - 49 = 0

Solve the equation

More Steps

Evaluate

24 x^{2} - 49 = 0

Move the constant to the right-hand side and change its sign

24 x^{2} = 0 + 49

Removing 0 doesn't change the value,so remove it from the expression

24 x^{2} = 49

Divide both sides

\frac{24 x ^{2}}{24} = \frac{49}{24}

Divide the numbers

x^{2} = \frac{49}{24}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{49}{24}

Simplify the expression

More Steps

Evaluate

\frac{49}{24}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{49}{24}

Simplify the radical expression

\frac{7}{24}

Simplify the radical expression

\frac{7}{2 6}

Multiply by the Conjugate

\frac{7 6}{2 6 \times 6}

Multiply the numbers

\frac{7 6}{12}

x = \pm \frac{7 6}{12}

Separate the equation into 2 possible cases

x = \frac{7 6}{12} x = - \frac{7 6}{12}

x = 0 x = \frac{7 6}{12} x = - \frac{7 6}{12}

Solution

x_{1} = - \frac{7 6}{12}, x_{2} = 0, x_{3} = \frac{7 6}{12}

Alternative Form

x_{1} \approx - 1.428869, x_{2} = 0, x_{3} \approx 1.428869

Show Solution