Solve x 7x-5 - ScanMath

Question

Simplify the expression

7 x^{2} - 5

Evaluate

x \times 7 x - 5

Solution

More Steps

Evaluate

x \times 7 x

Multiply the terms

x^{2} \times 7

Use the commutative property to reorder the terms

7 x^{2}

7 x^{2} - 5

Show Solution

x_{1} = - \frac{35}{7}, x_{2} = \frac{35}{7}

Alternative Form

x_{1} \approx - 0.845154, x_{2} \approx 0.845154

Evaluate

x \times 7 x - 5

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

x \times 7 x - 5 = 0

Multiply

More Steps

Multiply the terms

x \times 7 x

Multiply the terms

x^{2} \times 7

Use the commutative property to reorder the terms

7 x^{2}

7 x^{2} - 5 = 0

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

7 x^{2} = 0 + 5

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

7 x^{2} = 5

Divide both sides

\frac{7 x ^{2}}{7} = \frac{5}{7}

Divide the numbers

x^{2} = \frac{5}{7}

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

x = \pm \frac{5}{7}

Simplify the expression

More Steps

Evaluate

\frac{5}{7}

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

\frac{5}{7}

Multiply by the Conjugate

\frac{5 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

5 \times 7

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

5 \times 7

Calculate the product

35

\frac{35}{7 \times 7}

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

\frac{35}{7}

x = \pm \frac{35}{7}

Separate the equation into 2 possible cases

x = \frac{35}{7} x = - \frac{35}{7}

Solution

x_{1} = - \frac{35}{7}, x_{2} = \frac{35}{7}

Alternative Form

x_{1} \approx - 0.845154, x_{2} \approx 0.845154

Show Solution