Solve 8*5 - (105)*x^2 - Socratic AI (ScanMath)

Question

Simplify the expression

40 - 105 x^{2}

Evaluate

8 \times 5 - 105 x^{2}

Solution

40 - 105 x^{2}

Show Solution

5 (8 - 21 x^{2})

Evaluate

8 \times 5 - 105 x^{2}

Multiply the numbers

40 - 105 x^{2}

Solution

5 (8 - 21 x^{2})

Show Solution

x_{1} = - \frac{2 42}{21}, x_{2} = \frac{2 42}{21}

Alternative Form

x_{1} \approx - 0.617213, x_{2} \approx 0.617213

Evaluate

8 \times 5 - 105 x^{2}

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

8 \times 5 - 105 x^{2} = 0

Multiply the numbers

40 - 105 x^{2} = 0

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

- 105 x^{2} = 0 - 40

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

- 105 x^{2} = - 40

Change the signs on both sides of the equation

105 x^{2} = 40

Divide both sides

\frac{105 x ^{2}}{105} = \frac{40}{105}

Divide the numbers

x^{2} = \frac{40}{105}

Cancel out the common factor 5

x^{2} = \frac{8}{21}

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

x = \pm \frac{8}{21}

Simplify the expression

More Steps

Evaluate

\frac{8}{21}

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

\frac{8}{21}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{2 2}{21}

Multiply by the Conjugate

\frac{2 2 \times 21}{21 \times 21}

Multiply the numbers

More Steps

Evaluate

2 \times 21

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

2 \times 21

Calculate the product

42

\frac{2 42}{21 \times 21}

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

\frac{2 42}{21}

x = \pm \frac{2 42}{21}

Separate the equation into 2 possible cases

x = \frac{2 42}{21} x = - \frac{2 42}{21}

Solution

x_{1} = - \frac{2 42}{21}, x_{2} = \frac{2 42}{21}

Alternative Form

x_{1} \approx - 0.617213, x_{2} \approx 0.617213

Show Solution