Solve k^202-2002-1

Question

Simplify the expression

2 k^{2} - 2003

Evaluate

k^{2} \times 2 - 2002 - 1

Use the commutative property to reorder the terms

2 k^{2} - 2002 - 1

Solution

2 k^{2} - 2003

Show Solution

k_{1} = - \frac{4006}{2}, k_{2} = \frac{4006}{2}

Alternative Form

k_{1} \approx - 31.646485, k_{2} \approx 31.646485

Evaluate

k^{2} \times 2 - 2002 - 1

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

k^{2} \times 2 - 2002 - 1 = 0

Use the commutative property to reorder the terms

2 k^{2} - 2002 - 1 = 0

Subtract the numbers

2 k^{2} - 2003 = 0

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

2 k^{2} = 0 + 2003

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

2 k^{2} = 2003

Divide both sides

\frac{2 k ^{2}}{2} = \frac{2003}{2}

Divide the numbers

k^{2} = \frac{2003}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

k = \pm \frac{2003}{2}

Simplify the expression

More Steps

Evaluate

\frac{2003}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{2003}{2}

Multiply by the Conjugate

\frac{2003 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

2003 \times 2

The product of roots with the same index is equal to the root of the product

2003 \times 2

Calculate the product

4006

\frac{4006}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4006}{2}

k = \pm \frac{4006}{2}

Separate the equation into 2 possible cases

k = \frac{4006}{2} k = - \frac{4006}{2}

Solution

k_{1} = - \frac{4006}{2}, k_{2} = \frac{4006}{2}

Alternative Form

k_{1} \approx - 31.646485, k_{2} \approx 31.646485

Show Solution