Solve j^239-50-5138

Question

Simplify the expression

39 j^{2} - 5188

Evaluate

j^{2} \times 39 - 50 - 5138

Use the commutative property to reorder the terms

39 j^{2} - 50 - 5138

Solution

39 j^{2} - 5188

Show Solution

j_{1} = - \frac{2 50583}{39}, j_{2} = \frac{2 50583}{39}

Alternative Form

j_{1} \approx - 11.533674, j_{2} \approx 11.533674

Evaluate

j^{2} \times 39 - 50 - 5138

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

j^{2} \times 39 - 50 - 5138 = 0

Use the commutative property to reorder the terms

39 j^{2} - 50 - 5138 = 0

Subtract the numbers

39 j^{2} - 5188 = 0

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

39 j^{2} = 0 + 5188

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

39 j^{2} = 5188

Divide both sides

\frac{39 j ^{2}}{39} = \frac{5188}{39}

Divide the numbers

j^{2} = \frac{5188}{39}

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

j = \pm \frac{5188}{39}

Simplify the expression

More Steps

Evaluate

\frac{5188}{39}

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

\frac{5188}{39}

Simplify the radical expression

More Steps

Evaluate

5188

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

4 \times 1297

Write the number in exponential form with the base of 2

2^{2} \times 1297

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

2^{2} \times 1297

Reduce the index of the radical and exponent with 2

21297

\frac{2 1297}{39}

Multiply by the Conjugate

\frac{2 1297 \times 39}{39 \times 39}

Multiply the numbers

More Steps

Evaluate

1297 \times 39

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

1297 \times 39

Calculate the product

50583

\frac{2 50583}{39 \times 39}

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

\frac{2 50583}{39}

j = \pm \frac{2 50583}{39}

Separate the equation into 2 possible cases

j = \frac{2 50583}{39} j = - \frac{2 50583}{39}

Solution

j_{1} = - \frac{2 50583}{39}, j_{2} = \frac{2 50583}{39}

Alternative Form

j_{1} \approx - 11.533674, j_{2} \approx 11.533674

Show Solution