Solve j^21854-1 - ScanMath

Question

Simplify the expression

1854 j^{2} - 1

Evaluate

j^{2} \times 1854 - 1

Solution

1854 j^{2} - 1

Show Solution

j_{1} = - \frac{206}{618}, j_{2} = \frac{206}{618}

Alternative Form

j_{1} \approx - 0.023224, j_{2} \approx 0.023224

Evaluate

j^{2} \times 1854 - 1

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

j^{2} \times 1854 - 1 = 0

Use the commutative property to reorder the terms

1854 j^{2} - 1 = 0

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

1854 j^{2} = 0 + 1

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

1854 j^{2} = 1

Divide both sides

\frac{1854 j ^{2}}{1854} = \frac{1}{1854}

Divide the numbers

j^{2} = \frac{1}{1854}

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

j = \pm \frac{1}{1854}

Simplify the expression

More Steps

Evaluate

\frac{1}{1854}

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

\frac{1}{1854}

Simplify the radical expression

\frac{1}{1854}

Simplify the radical expression

More Steps

Evaluate

1854

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

9 \times 206

Write the number in exponential form with the base of 3

3^{2} \times 206

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

3^{2} \times 206

Reduce the index of the radical and exponent with 2

3206

\frac{1}{3 206}

Multiply by the Conjugate

\frac{206}{3 206 \times 206}

Multiply the numbers

More Steps

Evaluate

3206 \times 206

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

3 \times 206

Multiply the terms

618

\frac{206}{618}

j = \pm \frac{206}{618}

Separate the equation into 2 possible cases

j = \frac{206}{618} j = - \frac{206}{618}

Solution

j_{1} = - \frac{206}{618}, j_{2} = \frac{206}{618}

Alternative Form

j_{1} \approx - 0.023224, j_{2} \approx 0.023224

Show Solution