Solve g^2589-20043

Question

Simplify the expression

589 g^{2} - 20043

Evaluate

g^{2} \times 589 - 20043

Solution

589 g^{2} - 20043

Show Solution

g_{1} = - \frac{3 1311703}{589}, g_{2} = \frac{3 1311703}{589}

Alternative Form

g_{1} \approx - 5.833426, g_{2} \approx 5.833426

Evaluate

g^{2} \times 589 - 20043

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

g^{2} \times 589 - 20043 = 0

Use the commutative property to reorder the terms

589 g^{2} - 20043 = 0

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

589 g^{2} = 0 + 20043

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

589 g^{2} = 20043

Divide both sides

\frac{589 g ^{2}}{589} = \frac{20043}{589}

Divide the numbers

g^{2} = \frac{20043}{589}

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

g = \pm \frac{20043}{589}

Simplify the expression

More Steps

Evaluate

\frac{20043}{589}

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

\frac{20043}{589}

Simplify the radical expression

More Steps

Evaluate

20043

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

9 \times 2227

Write the number in exponential form with the base of 3

3^{2} \times 2227

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

3^{2} \times 2227

Reduce the index of the radical and exponent with 2

32227

\frac{3 2227}{589}

Multiply by the Conjugate

\frac{3 2227 \times 589}{589 \times 589}

Multiply the numbers

More Steps

Evaluate

2227 \times 589

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

2227 \times 589

Calculate the product

1311703

\frac{3 1311703}{589 \times 589}

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

\frac{3 1311703}{589}

g = \pm \frac{3 1311703}{589}

Separate the equation into 2 possible cases

g = \frac{3 1311703}{589} g = - \frac{3 1311703}{589}

Solution

g_{1} = - \frac{3 1311703}{589}, g_{2} = \frac{3 1311703}{589}

Alternative Form

g_{1} \approx - 5.833426, g_{2} \approx 5.833426

Show Solution