Solve 7x^2 3 - 5(x^2 - 4)

Question

Simplify the expression

16 x^{2} + 20

Evaluate

7 x^{2} \times 3 - 5 (x^{2} - 4)

Multiply the terms

21 x^{2} - 5 (x^{2} - 4)

Expand the expression

More Steps

Calculate

- 5 (x^{2} - 4)

Apply the distributive property

- 5 x^{2} - (- 5 \times 4)

Multiply the numbers

- 5 x^{2} - (- 20)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 5 x^{2} + 20

21 x^{2} - 5 x^{2} + 20

Solution

More Steps

Evaluate

21 x^{2} - 5 x^{2}

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

(21 - 5) x^{2}

Subtract the numbers

16 x^{2}

16 x^{2} + 20

Show Solution

Factor the expression

4 (4 x^{2} + 5)

Evaluate

7 x^{2} \times 3 - 5 (x^{2} - 4)

Multiply the terms

21 x^{2} - 5 (x^{2} - 4)

Simplify

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Evaluate

- 5 (x^{2} - 4)

Apply the distributive property

- 5 x^{2} - 5 (- 4)

Multiply the terms

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Evaluate

- 5 (- 4)

Multiplying or dividing an even number of negative terms equals a positive

5 \times 4

Multiply the numbers

20

- 5 x^{2} + 20

21 x^{2} - 5 x^{2} + 20

Subtract the terms

More Steps

Evaluate

21 x^{2} - 5 x^{2}

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

(21 - 5) x^{2}

Subtract the numbers

16 x^{2}

16 x^{2} + 20

Solution

4 (4 x^{2} + 5)

Show Solution

Find the roots

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

Alternative Form

x_{1} \approx - 1.118034 i, x_{2} \approx 1.118034 i

Evaluate

7 x^{2} \times 3 - 5 (x^{2} - 4)

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

7 x^{2} \times 3 - 5 (x^{2} - 4) = 0

Multiply the terms

21 x^{2} - 5 (x^{2} - 4) = 0

Calculate

More Steps

Evaluate

21 x^{2} - 5 (x^{2} - 4)

Expand the expression

More Steps

Calculate

- 5 (x^{2} - 4)

Apply the distributive property

- 5 x^{2} - (- 5 \times 4)

Multiply the numbers

- 5 x^{2} - (- 20)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 5 x^{2} + 20

21 x^{2} - 5 x^{2} + 20

Subtract the terms

More Steps

Evaluate

21 x^{2} - 5 x^{2}

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

(21 - 5) x^{2}

Subtract the numbers

16 x^{2}

16 x^{2} + 20

16 x^{2} + 20 = 0

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

16 x^{2} = 0 - 20

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

16 x^{2} = - 20

Divide both sides

\frac{16 x ^{2}}{16} = \frac{- 20}{16}

Divide the numbers

x^{2} = \frac{- 20}{16}

Divide the numbers

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Evaluate

\frac{- 20}{16}

Cancel out the common factor 4

\frac{- 5}{4}

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

- \frac{5}{4}

x^{2} = - \frac{5}{4}

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

x = \pm - \frac{5}{4}

Simplify the expression

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Evaluate

- \frac{5}{4}

Evaluate the power

\frac{5}{4} \times - 1

Evaluate the power

\frac{5}{4} \times i

Evaluate the power

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Evaluate

\frac{5}{4}

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

\frac{5}{4}

Simplify the radical expression

\frac{5}{2}

\frac{5}{2} i

x = \pm \frac{5}{2} i

Separate the equation into 2 possible cases

x = \frac{5}{2} i x = - \frac{5}{2} i

Solution

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

Alternative Form

x_{1} \approx - 1.118034 i, x_{2} \approx 1.118034 i

Show Solution