Solve 2x^2-3x-9/4x^2-9

Question

Simplify the expression

- \frac{1}{4} x^{2} - 3 x - 9

Evaluate

2 x^{2} - 3 x - \frac{9}{4} x^{2} - 9

Solution

More Steps

Evaluate

2 x^{2} - \frac{9}{4} x^{2}

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

(2 - \frac{9}{4}) x^{2}

Subtract the numbers

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Evaluate

2 - \frac{9}{4}

Reduce fractions to a common denominator

\frac{2 \times 4}{4} - \frac{9}{4}

Write all numerators above the common denominator

\frac{2 \times 4 - 9}{4}

Multiply the numbers

\frac{8 - 9}{4}

Subtract the numbers

\frac{- 1}{4}

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

- \frac{1}{4}

- \frac{1}{4} x^{2}

- \frac{1}{4} x^{2} - 3 x - 9

Show Solution

- \frac{1}{4} (x + 6)^{2}

Evaluate

2 x^{2} - 3 x - \frac{9}{4} x^{2} - 9

Subtract the terms

More Steps

Evaluate

2 x^{2} - \frac{9}{4} x^{2}

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

(2 - \frac{9}{4}) x^{2}

Subtract the numbers

More Steps

Evaluate

2 - \frac{9}{4}

Reduce fractions to a common denominator

\frac{2 \times 4}{4} - \frac{9}{4}

Write all numerators above the common denominator

\frac{2 \times 4 - 9}{4}

Multiply the numbers

\frac{8 - 9}{4}

Subtract the numbers

\frac{- 1}{4}

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

- \frac{1}{4}

- \frac{1}{4} x^{2}

- \frac{1}{4} x^{2} - 3 x - 9

Solution

- \frac{1}{4} (x + 6)^{2}

Show Solution

x = - 6

Evaluate

2 x^{2} - 3 x - \frac{9}{4} x^{2} - 9

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

2 x^{2} - 3 x - \frac{9}{4} x^{2} - 9 = 0

Subtract the terms

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Simplify

2 x^{2} - 3 x - \frac{9}{4} x^{2}

Subtract the terms

More Steps

Evaluate

2 x^{2} - \frac{9}{4} x^{2}

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

(2 - \frac{9}{4}) x^{2}

Subtract the numbers

- \frac{1}{4} x^{2}

- \frac{1}{4} x^{2} - 3 x

- \frac{1}{4} x^{2} - 3 x - 9 = 0

Use a^{2} + 2 ab + b^{2} = (a + b)^{2} to factor the expression

- \frac{1}{4} (x + 6)^{2} = 0

Divide the terms

(x + 6)^{2} = 0

Simplify the expression

x + 6 = 0

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

x = 0 - 6

Solution

x = - 6

Show Solution