Solve t^2-2t-400 - ScanMath

Question

Find the roots

t_{1} = 1 - 401, t_{2} = 1 + 401

Alternative Form

t_{1} \approx - 19.024984, t_{2} \approx 21.024984

Evaluate

t^{2} - 2 t - 400

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

t^{2} - 2 t - 400 = 0

Substitute a= 1,b= - 2 and c= - 400 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 400 )}{2}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 (- 400)

Multiply the numbers

More Steps

Evaluate

4 (- 400)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 400

Multiply the numbers

- 1600

(- 2)^{2} - (- 1600)

Rewrite the expression

2^{2} - (- 1600)

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

2^{2} + 1600

Evaluate the power

4 + 1600

Add the numbers

1604

t = \frac{2 \pm 1604}{2}

Simplify the radical expression

More Steps

Evaluate

1604

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

4 \times 401

Write the number in exponential form with the base of 2

2^{2} \times 401

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

2^{2} \times 401

Reduce the index of the radical and exponent with 2

2401

t = \frac{2 \pm 2 401}{2}

Separate the equation into 2 possible cases

t = \frac{2 + 2 401}{2} t = \frac{2 - 2 401}{2}

Simplify the expression

More Steps

Evaluate

t = \frac{2 + 2 401}{2}

Divide the terms

More Steps

Evaluate

\frac{2 + 2 401}{2}

Rewrite the expression

\frac{2 ( 1 + 401 )}{2}

Reduce the fraction

1 + 401

t = 1 + 401

t = 1 + 401 t = \frac{2 - 2 401}{2}

Simplify the expression

More Steps

Evaluate

t = \frac{2 - 2 401}{2}

Divide the terms

More Steps

Evaluate

\frac{2 - 2 401}{2}

Rewrite the expression

\frac{2 ( 1 - 401 )}{2}

Reduce the fraction

1 - 401

t = 1 - 401

t = 1 + 401 t = 1 - 401

Solution

t_{1} = 1 - 401, t_{2} = 1 + 401

Alternative Form

t_{1} \approx - 19.024984, t_{2} \approx 21.024984

Show Solution