Solve 2(x^21x^2)-7(x 1x) 9=0

Question

Solve the equation

x_{1} = - \frac{3 14}{2}, x_{2} = 0, x_{3} = \frac{3 14}{2}

Alternative Form

x_{1} \approx - 5.612486, x_{2} = 0, x_{3} \approx 5.612486

Evaluate

2 (x^{2} \times 1 \times x^{2}) - 7 (x \times 1 \times x) \times 9 = 0

Remove the parentheses

2 x^{2} \times 1 \times x^{2} - 7 x \times 1 \times x \times 9 = 0

Simplify

More Steps

Evaluate

2 x^{2} \times 1 \times x^{2} - 7 x \times 1 \times x \times 9

Multiply the terms

More Steps

Multiply the terms

2 x^{2} \times 1 \times x^{2}

Rewrite the expression

2 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

2 x^{2 + 2}

Add the numbers

2 x^{4}

2 x^{4} - 7 x \times 1 \times x \times 9

Multiply the terms

More Steps

Multiply the terms

7 x \times 1 \times x \times 9

Rewrite the expression

7 x \times x \times 9

Multiply the terms

63 x \times x

Multiply the terms

63 x^{2}

2 x^{4} - 63 x^{2}

2 x^{4} - 63 x^{2} = 0

Factor the expression

x^{2} (2 x^{2} - 63) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{2} - 63 = 0

The only way a power can be 0 is when the base equals 0

x = 0 2 x^{2} - 63 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 63 = 0

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

2 x^{2} = 0 + 63

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

2 x^{2} = 63

Divide both sides

\frac{2 x ^{2}}{2} = \frac{63}{2}

Divide the numbers

x^{2} = \frac{63}{2}

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

x = \pm \frac{63}{2}

Simplify the expression

More Steps

Evaluate

\frac{63}{2}

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

\frac{63}{2}

Simplify the radical expression

\frac{3 7}{2}

Multiply by the Conjugate

\frac{3 7 \times 2}{2 \times 2}

Multiply the numbers

\frac{3 14}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3 14}{2}

x = \pm \frac{3 14}{2}

Separate the equation into 2 possible cases

x = \frac{3 14}{2} x = - \frac{3 14}{2}

x = 0 x = \frac{3 14}{2} x = - \frac{3 14}{2}

Solution

x_{1} = - \frac{3 14}{2}, x_{2} = 0, x_{3} = \frac{3 14}{2}

Alternative Form

x_{1} \approx - 5.612486, x_{2} = 0, x_{3} \approx 5.612486

Show Solution