Solve 3x^2+13x-10/9x^2-4

Question

Simplify the expression

\frac{17}{9} x^{2} + 13 x - 4

Evaluate

3 x^{2} + 13 x - \frac{10}{9} x^{2} - 4

Solution

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Evaluate

3 x^{2} - \frac{10}{9} x^{2}

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

(3 - \frac{10}{9}) x^{2}

Subtract the numbers

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Evaluate

3 - \frac{10}{9}

Reduce fractions to a common denominator

\frac{3 \times 9}{9} - \frac{10}{9}

Write all numerators above the common denominator

\frac{3 \times 9 - 10}{9}

Multiply the numbers

\frac{27 - 10}{9}

Subtract the numbers

\frac{17}{9}

\frac{17}{9} x^{2}

\frac{17}{9} x^{2} + 13 x - 4

Show Solution

Factor the expression

\frac{1}{9} (17 x^{2} + 117 x - 36)

Evaluate

3 x^{2} + 13 x - \frac{10}{9} x^{2} - 4

Subtract the terms

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Evaluate

3 x^{2} - \frac{10}{9} x^{2}

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

(3 - \frac{10}{9}) x^{2}

Subtract the numbers

More Steps

Evaluate

3 - \frac{10}{9}

Reduce fractions to a common denominator

\frac{3 \times 9}{9} - \frac{10}{9}

Write all numerators above the common denominator

\frac{3 \times 9 - 10}{9}

Multiply the numbers

\frac{27 - 10}{9}

Subtract the numbers

\frac{17}{9}

\frac{17}{9} x^{2}

\frac{17}{9} x^{2} + 13 x - 4

Solution

\frac{1}{9} (17 x^{2} + 117 x - 36)

Show Solution

Find the roots

x_{1} = - \frac{117 + 3 1793}{34}, x_{2} = \frac{- 117 + 3 1793}{34}

Alternative Form

x_{1} \approx - 7.177397, x_{2} \approx 0.295044

Evaluate

3 x^{2} + 13 x - \frac{10}{9} x^{2} - 4

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

3 x^{2} + 13 x - \frac{10}{9} x^{2} - 4 = 0

Subtract the terms

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Simplify

3 x^{2} + 13 x - \frac{10}{9} x^{2}

Subtract the terms

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Evaluate

3 x^{2} - \frac{10}{9} x^{2}

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

(3 - \frac{10}{9}) x^{2}

Subtract the numbers

\frac{17}{9} x^{2}

\frac{17}{9} x^{2} + 13 x

\frac{17}{9} x^{2} + 13 x - 4 = 0

Multiply both sides

9 (\frac{17}{9} x^{2} + 13 x - 4) = 9 \times 0

Calculate

17 x^{2} + 117 x - 36 = 0

Substitute a= 17,b= 117 and c= - 36 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 117 \pm 11 7 ^{2} - 4 \times 17 ( - 36 )}{2 \times 17}

Simplify the expression

x = \frac{- 117 \pm 11 7 ^{2} - 4 \times 17 ( - 36 )}{34}

Simplify the expression

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Evaluate

11 7^{2} - 4 \times 17 (- 36)

Multiply

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Multiply the terms

4 \times 17 (- 36)

Rewrite the expression

- 4 \times 17 \times 36

Multiply the terms

- 2448

11 7^{2} - (- 2448)

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

11 7^{2} + 2448

Evaluate the power

13689 + 2448

Add the numbers

16137

x = \frac{- 117 \pm 16137}{34}

Simplify the radical expression

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Evaluate

16137

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

9 \times 1793

Write the number in exponential form with the base of 3

3^{2} \times 1793

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

3^{2} \times 1793

Reduce the index of the radical and exponent with 2

31793

x = \frac{- 117 \pm 3 1793}{34}

Separate the equation into 2 possible cases

x = \frac{- 117 + 3 1793}{34} x = \frac{- 117 - 3 1793}{34}

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

x = \frac{- 117 + 3 1793}{34} x = - \frac{117 + 3 1793}{34}

Solution

x_{1} = - \frac{117 + 3 1793}{34}, x_{2} = \frac{- 117 + 3 1793}{34}

Alternative Form

x_{1} \approx - 7.177397, x_{2} \approx 0.295044

Show Solution