Solve q^2232-80003

Question

Simplify the expression

232 q^{2} - 80003

Evaluate

q^{2} \times 232 - 80003

Solution

232 q^{2} - 80003

Show Solution

q_{1} = - \frac{4640174}{116}, q_{2} = \frac{4640174}{116}

Alternative Form

q_{1} \approx - 18.569882, q_{2} \approx 18.569882

Evaluate

q^{2} \times 232 - 80003

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

q^{2} \times 232 - 80003 = 0

Use the commutative property to reorder the terms

232 q^{2} - 80003 = 0

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

232 q^{2} = 0 + 80003

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

232 q^{2} = 80003

Divide both sides

\frac{232 q ^{2}}{232} = \frac{80003}{232}

Divide the numbers

q^{2} = \frac{80003}{232}

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

q = \pm \frac{80003}{232}

Simplify the expression

More Steps

Evaluate

\frac{80003}{232}

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

\frac{80003}{232}

Simplify the radical expression

More Steps

Evaluate

232

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

4 \times 58

Write the number in exponential form with the base of 2

2^{2} \times 58

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

2^{2} \times 58

Reduce the index of the radical and exponent with 2

258

\frac{80003}{2 58}

Multiply by the Conjugate

\frac{80003 \times 58}{2 58 \times 58}

Multiply the numbers

More Steps

Evaluate

80003 \times 58

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

80003 \times 58

Calculate the product

4640174

\frac{4640174}{2 58 \times 58}

Multiply the numbers

More Steps

Evaluate

258 \times 58

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

2 \times 58

Multiply the terms

116

\frac{4640174}{116}

q = \pm \frac{4640174}{116}

Separate the equation into 2 possible cases

q = \frac{4640174}{116} q = - \frac{4640174}{116}

Solution

q_{1} = - \frac{4640174}{116}, q_{2} = \frac{4640174}{116}

Alternative Form

q_{1} \approx - 18.569882, q_{2} \approx 18.569882

Show Solution