Solve 1206-4m^2 - ScanMath

Question

Factor the expression

2 (603 - 2 m^{2})

Evaluate

1206 - 4 m^{2}

Solution

2 (603 - 2 m^{2})

Show Solution

m_{1} = - \frac{3 134}{2}, m_{2} = \frac{3 134}{2}

Alternative Form

m_{1} \approx - 17.363755, m_{2} \approx 17.363755

Evaluate

1206 - 4 m^{2}

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

1206 - 4 m^{2} = 0

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

- 4 m^{2} = 0 - 1206

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

- 4 m^{2} = - 1206

Change the signs on both sides of the equation

4 m^{2} = 1206

Divide both sides

\frac{4 m ^{2}}{4} = \frac{1206}{4}

Divide the numbers

m^{2} = \frac{1206}{4}

Cancel out the common factor 2

m^{2} = \frac{603}{2}

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

m = \pm \frac{603}{2}

Simplify the expression

More Steps

Evaluate

\frac{603}{2}

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

\frac{603}{2}

Simplify the radical expression

More Steps

Evaluate

603

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

9 \times 67

Write the number in exponential form with the base of 3

3^{2} \times 67

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

3^{2} \times 67

Reduce the index of the radical and exponent with 2

367

\frac{3 67}{2}

Multiply by the Conjugate

\frac{3 67 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

67 \times 2

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

67 \times 2

Calculate the product

134

\frac{3 134}{2 \times 2}

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

\frac{3 134}{2}

m = \pm \frac{3 134}{2}

Separate the equation into 2 possible cases

m = \frac{3 134}{2} m = - \frac{3 134}{2}

Solution

m_{1} = - \frac{3 134}{2}, m_{2} = \frac{3 134}{2}

Alternative Form

m_{1} \approx - 17.363755, m_{2} \approx 17.363755

Show Solution