Solve 7x ^ 2 - 6 - 2x ^ 2

Question

Simplify the expression

5 x^{2} - 6

Evaluate

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

Solution

More Steps

Evaluate

7 x^{2} - 2 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(7 - 2) x^{2}

Subtract the numbers

5 x^{2}

5 x^{2} - 6

Show Solution

x_{1} = - \frac{30}{5}, x_{2} = \frac{30}{5}

Alternative Form

x_{1} \approx - 1.095445, x_{2} \approx 1.095445

Evaluate

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

To find the roots of the expression,set the expression equal to 0

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

Subtract the terms

More Steps

Simplify

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

Subtract the terms

More Steps

Evaluate

7 x^{2} - 2 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(7 - 2) x^{2}

Subtract the numbers

5 x^{2}

5 x^{2} - 6

5 x^{2} - 6 = 0

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

5 x^{2} = 0 + 6

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

5 x^{2} = 6

Divide both sides

\frac{5 x ^{2}}{5} = \frac{6}{5}

Divide the numbers

x^{2} = \frac{6}{5}

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

x = \pm \frac{6}{5}

Simplify the expression

More Steps

Evaluate

\frac{6}{5}

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

\frac{6}{5}

Multiply by the Conjugate

\frac{6 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

6 \times 5

The product of roots with the same index is equal to the root of the product

6 \times 5

Calculate the product

30

\frac{30}{5 \times 5}

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

\frac{30}{5}

x = \pm \frac{30}{5}

Separate the equation into 2 possible cases

x = \frac{30}{5} x = - \frac{30}{5}

Solution

x_{1} = - \frac{30}{5}, x_{2} = \frac{30}{5}

Alternative Form

x_{1} \approx - 1.095445, x_{2} \approx 1.095445

Show Solution