Solve -5t^2+40t+10=45

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

t_{1} = 1, t_{2} = 7

Evaluate

- 5 t^{2} + 40 t + 10 = 45

Move the expression to the left side

- 5 t^{2} + 40 t - 35 = 0

Factor the expression

More Steps

Evaluate

- 5 t^{2} + 40 t - 35

Rewrite the expression

- 5 t^{2} + 5 \times 8 t - 5 \times 7

Factor out - 5 from the expression

- 5 (t^{2} - 8 t + 7)

Factor the expression

More Steps

Evaluate

t^{2} - 8 t + 7

Rewrite the expression

t^{2} + (- 1 - 7) t + 7

Calculate

t^{2} - t - 7 t + 7

Rewrite the expression

t \times t - t - 7 t + 7

Factor out t from the expression

t (t - 1) - 7 t + 7

Factor out - 7 from the expression

t (t - 1) - 7 (t - 1)

Factor out t - 1 from the expression

(t - 7) (t - 1)

- 5 (t - 7) (t - 1)

- 5 (t - 7) (t - 1) = 0

Divide the terms

(t - 7) (t - 1) = 0

When the product of factors equals 0,at least one factor is 0

t - 7 = 0 t - 1 = 0

Solve the equation for t

More Steps

Evaluate

t - 7 = 0

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

t = 0 + 7

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

t = 7

t = 7 t - 1 = 0

Solve the equation for t

More Steps

Evaluate

t - 1 = 0

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

t = 0 + 1

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

t = 1

t = 7 t = 1

Solution

t_{1} = 1, t_{2} = 7

Show Solution