Solve 5(x 7)^2-2 - ScanMath

Question

Simplify the expression

245 x^{2} - 2

Evaluate

5 (x \times 7)^{2} - 2

Use the commutative property to reorder the terms

5 (7 x)^{2} - 2

Solution

More Steps

Evaluate

5 (7 x)^{2}

Rewrite the expression

5 \times 49 x^{2}

Multiply the numbers

245 x^{2}

245 x^{2} - 2

Show Solution

x_{1} = - \frac{10}{35}, x_{2} = \frac{10}{35}

Alternative Form

x_{1} \approx - 0.090351, x_{2} \approx 0.090351

Evaluate

5 (x \times 7)^{2} - 2

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

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

Use the commutative property to reorder the terms

5 (7 x)^{2} - 2 = 0

Multiply the terms

More Steps

Evaluate

5 (7 x)^{2}

Rewrite the expression

5 \times 49 x^{2}

Multiply the numbers

245 x^{2}

245 x^{2} - 2 = 0

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

245 x^{2} = 0 + 2

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

245 x^{2} = 2

Divide both sides

\frac{245 x ^{2}}{245} = \frac{2}{245}

Divide the numbers

x^{2} = \frac{2}{245}

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

x = \pm \frac{2}{245}

Simplify the expression

More Steps

Evaluate

\frac{2}{245}

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

\frac{2}{245}

Simplify the radical expression

More Steps

Evaluate

245

Write the expression as a product where the root of one of the factors can be evaluated

49 \times 5

Write the number in exponential form with the base of 7

7^{2} \times 5

The root of a product is equal to the product of the roots of each factor

7^{2} \times 5

Reduce the index of the radical and exponent with 2

75

\frac{2}{7 5}

Multiply by the Conjugate

\frac{2 \times 5}{7 5 \times 5}

Multiply the numbers

More Steps

Evaluate

2 \times 5

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

2 \times 5

Calculate the product

10

\frac{10}{7 5 \times 5}

Multiply the numbers

More Steps

Evaluate

75 \times 5

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

7 \times 5

Multiply the terms

35

\frac{10}{35}

x = \pm \frac{10}{35}

Separate the equation into 2 possible cases

x = \frac{10}{35} x = - \frac{10}{35}

Solution

x_{1} = - \frac{10}{35}, x_{2} = \frac{10}{35}

Alternative Form

x_{1} \approx - 0.090351, x_{2} \approx 0.090351

Show Solution