Solve -7x^(2)+12x-8+3x^(2)+9x-5

Question

Simplify the expression

Solution

- 4 x^{2} + 21 x - 13

Evaluate

- 7 x^{2} + 12 x - 8 + 3 x^{2} + 9 x - 5

Add the terms

More Steps

Evaluate

- 7 x^{2} + 3 x^{2}

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

(- 7 + 3) x^{2}

Add the numbers

- 4 x^{2}

- 4 x^{2} + 12 x - 8 + 9 x - 5

Add the terms

More Steps

Evaluate

12 x + 9 x

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

(12 + 9) x

Add the numbers

21 x

- 4 x^{2} + 21 x - 8 - 5

Solution

- 4 x^{2} + 21 x - 13

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = \frac{21 - 233}{8}, x_{2} = \frac{21 + 233}{8}

Alternative Form

x_{1} \approx 0.716958, x_{2} \approx 4.533042

Evaluate

- 7 x^{2} + 12 x - 8 + 3 x^{2} + 9 x - 5

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

- 7 x^{2} + 12 x - 8 + 3 x^{2} + 9 x - 5 = 0

Calculate the sum or difference

More Steps

Evaluate

- 7 x^{2} + 12 x - 8 + 3 x^{2} + 9 x

Add the terms

More Steps

Evaluate

- 7 x^{2} + 3 x^{2}

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

(- 7 + 3) x^{2}

Add the numbers

- 4 x^{2}

- 4 x^{2} + 12 x - 8 + 9 x

Add the terms

More Steps

Evaluate

12 x + 9 x

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

(12 + 9) x

Add the numbers

21 x

- 4 x^{2} + 21 x - 8

- 4 x^{2} + 21 x - 8 - 5 = 0

Subtract the numbers

- 4 x^{2} + 21 x - 13 = 0

Multiply both sides

4 x^{2} - 21 x + 13 = 0

Substitute a= 4,b= - 21 and c= 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 4 \times 13}{2 \times 4}

Simplify the expression

x = \frac{21 \pm ( - 21 ) ^{2} - 4 \times 4 \times 13}{8}

Simplify the expression

More Steps

Evaluate

(- 21)^{2} - 4 \times 4 \times 13

Multiply the terms

More Steps

Multiply the terms

4 \times 4 \times 13

Multiply the terms

16 \times 13

Multiply the numbers

208

(- 21)^{2} - 208

Rewrite the expression

2 1^{2} - 208

Evaluate the power

441 - 208

Subtract the numbers

233

x = \frac{21 \pm 233}{8}

Separate the equation into 2 possible cases

x = \frac{21 + 233}{8} x = \frac{21 - 233}{8}

Solution

x_{1} = \frac{21 - 233}{8}, x_{2} = \frac{21 + 233}{8}

Alternative Form

x_{1} \approx 0.716958, x_{2} \approx 4.533042

Show Solution

7x^(2)+12x 8+3x^(2)+9x 5

Simplify the expression

Solution

Find the roots

Find the roots of the algebra expression