Solve 21x^2+53-8 - ScanMath

Question

Simplify the expression

21 x^{2} + 45

Evaluate

21 x^{2} + 53 - 8

Solution

21 x^{2} + 45

Show Solution

3 (7 x^{2} + 15)

Evaluate

21 x^{2} + 53 - 8

Subtract the numbers

21 x^{2} + 45

Solution

3 (7 x^{2} + 15)

Show Solution

x_{1} = - \frac{105}{7} i, x_{2} = \frac{105}{7} i

Alternative Form

x_{1} \approx - 1.46385 i, x_{2} \approx 1.46385 i

Evaluate

21 x^{2} + 53 - 8

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

21 x^{2} + 53 - 8 = 0

Subtract the numbers

21 x^{2} + 45 = 0

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

21 x^{2} = 0 - 45

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

21 x^{2} = - 45

Divide both sides

\frac{21 x ^{2}}{21} = \frac{- 45}{21}

Divide the numbers

x^{2} = \frac{- 45}{21}

Divide the numbers

More Steps

Evaluate

\frac{- 45}{21}

Cancel out the common factor 3

\frac{- 15}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{15}{7}

x^{2} = - \frac{15}{7}

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

x = \pm - \frac{15}{7}

Simplify the expression

More Steps

Evaluate

- \frac{15}{7}

Evaluate the power

\frac{15}{7} \times - 1

Evaluate the power

\frac{15}{7} \times i

Evaluate the power

More Steps

Evaluate

\frac{15}{7}

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

\frac{15}{7}

Multiply by the Conjugate

\frac{15 \times 7}{7 \times 7}

Multiply the numbers

\frac{105}{7 \times 7}

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

\frac{105}{7}

\frac{105}{7} i

x = \pm \frac{105}{7} i

Separate the equation into 2 possible cases

x = \frac{105}{7} i x = - \frac{105}{7} i

Solution

x_{1} = - \frac{105}{7} i, x_{2} = \frac{105}{7} i

Alternative Form

x_{1} \approx - 1.46385 i, x_{2} \approx 1.46385 i

Show Solution