Solve (8t^2-9t 7)-(2t-3)

Question

Simplify the expression

8 t^{2} - 65 t + 3

Evaluate

(8 t^{2} - 9 t \times 7) - (2 t - 3)

Multiply the terms

(8 t^{2} - 63 t) - (2 t - 3)

Remove the parentheses

8 t^{2} - 63 t - (2 t - 3)

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

8 t^{2} - 63 t - 2 t + 3

Solution

More Steps

Evaluate

- 63 t - 2 t

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

(- 63 - 2) t

Subtract the numbers

- 65 t

8 t^{2} - 65 t + 3

Show Solution

Find the roots

t_{1} = \frac{65 - 4129}{16}, t_{2} = \frac{65 + 4129}{16}

Alternative Form

t_{1} \approx 0.046419, t_{2} \approx 8.078581

Evaluate

(8 t^{2} - 9 t \times 7) - (2 t - 3)

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

(8 t^{2} - 9 t \times 7) - (2 t - 3) = 0

Multiply the terms

(8 t^{2} - 63 t) - (2 t - 3) = 0

Remove the parentheses

8 t^{2} - 63 t - (2 t - 3) = 0

Subtract the terms

More Steps

Simplify

8 t^{2} - 63 t - (2 t - 3)

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

8 t^{2} - 63 t - 2 t + 3

Subtract the terms

More Steps

Evaluate

- 63 t - 2 t

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

(- 63 - 2) t

Subtract the numbers

- 65 t

8 t^{2} - 65 t + 3

8 t^{2} - 65 t + 3 = 0

Substitute a= 8,b= - 65 and c= 3 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{65 \pm ( - 65 ) ^{2} - 4 \times 8 \times 3}{2 \times 8}

Simplify the expression

t = \frac{65 \pm ( - 65 ) ^{2} - 4 \times 8 \times 3}{16}

Simplify the expression

More Steps

Evaluate

(- 65)^{2} - 4 \times 8 \times 3

Multiply the terms

More Steps

Multiply the terms

4 \times 8 \times 3

Multiply the terms

32 \times 3

Multiply the numbers

96

(- 65)^{2} - 96

Rewrite the expression

6 5^{2} - 96

Evaluate the power

4225 - 96

Subtract the numbers

4129

t = \frac{65 \pm 4129}{16}

Separate the equation into 2 possible cases

t = \frac{65 + 4129}{16} t = \frac{65 - 4129}{16}

Solution

t_{1} = \frac{65 - 4129}{16}, t_{2} = \frac{65 + 4129}{16}

Alternative Form

t_{1} \approx 0.046419, t_{2} \approx 8.078581

Show Solution