Solve q^22e-e1301

Question

Simplify the expression

2 e q^{2} - 1301 e

Evaluate

q^{2} \times 2 e - e \times 1301

Multiply the terms

More Steps

Multiply the terms

q^{2} \times 2 e

Use the commutative property to reorder the terms

2 q^{2} e

Multiply the numbers

2 e q^{2}

2 e q^{2} - e \times 1301

Solution

2 e q^{2} - 1301 e

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Factor the expression

e (2 q^{2} - 1301)

Evaluate

q^{2} \times 2 e - e \times 1301

Multiply the terms

More Steps

Multiply the terms

q^{2} \times 2 e

Use the commutative property to reorder the terms

2 q^{2} e

Multiply the numbers

2 e q^{2}

2 e q^{2} - e \times 1301

Use the commutative property to reorder the terms

2 e q^{2} - 1301 e

Solution

e (2 q^{2} - 1301)

Show Solution

Find the roots

q_{1} = - \frac{2602}{2}, q_{2} = \frac{2602}{2}

Alternative Form

q_{1} \approx - 25.504901, q_{2} \approx 25.504901

Evaluate

q^{2} \times 2 e - e \times 1301

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

q^{2} \times 2 e - e \times 1301 = 0

Multiply the terms

More Steps

Multiply the terms

q^{2} \times 2 e

Use the commutative property to reorder the terms

2 q^{2} e

Multiply the numbers

2 e q^{2}

2 e q^{2} - e \times 1301 = 0

Use the commutative property to reorder the terms

2 e q^{2} - 1301 e = 0

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

2 e q^{2} = 0 + 1301 e

Add the terms

2 e q^{2} = 1301 e

Divide both sides

\frac{2 e q ^{2}}{2 e} = \frac{1301 e}{2 e}

Divide the numbers

q^{2} = \frac{1301 e}{2 e}

Divide the numbers

q^{2} = \frac{1301}{2}

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

q = \pm \frac{1301}{2}

Simplify the expression

More Steps

Evaluate

\frac{1301}{2}

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

\frac{1301}{2}

Multiply by the Conjugate

\frac{1301 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

1301 \times 2

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

1301 \times 2

Calculate the product

2602

\frac{2602}{2 \times 2}

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

\frac{2602}{2}

q = \pm \frac{2602}{2}

Separate the equation into 2 possible cases

q = \frac{2602}{2} q = - \frac{2602}{2}

Solution

q_{1} = - \frac{2602}{2}, q_{2} = \frac{2602}{2}

Alternative Form

q_{1} \approx - 25.504901, q_{2} \approx 25.504901

Show Solution