Solve n^243-64-43002

Question

Simplify the expression

43 n^{2} - 43066

Evaluate

n^{2} \times 43 - 64 - 43002

Use the commutative property to reorder the terms

43 n^{2} - 64 - 43002

Solution

43 n^{2} - 43066

Show Solution

n_{1} = - \frac{1851838}{43}, n_{2} = \frac{1851838}{43}

Alternative Form

n_{1} \approx - 31.647036, n_{2} \approx 31.647036

Evaluate

n^{2} \times 43 - 64 - 43002

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

n^{2} \times 43 - 64 - 43002 = 0

Use the commutative property to reorder the terms

43 n^{2} - 64 - 43002 = 0

Subtract the numbers

43 n^{2} - 43066 = 0

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

43 n^{2} = 0 + 43066

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

43 n^{2} = 43066

Divide both sides

\frac{43 n ^{2}}{43} = \frac{43066}{43}

Divide the numbers

n^{2} = \frac{43066}{43}

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

n = \pm \frac{43066}{43}

Simplify the expression

More Steps

Evaluate

\frac{43066}{43}

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

\frac{43066}{43}

Multiply by the Conjugate

\frac{43066 \times 43}{43 \times 43}

Multiply the numbers

More Steps

Evaluate

43066 \times 43

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

43066 \times 43

Calculate the product

1851838

\frac{1851838}{43 \times 43}

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

\frac{1851838}{43}

n = \pm \frac{1851838}{43}

Separate the equation into 2 possible cases

n = \frac{1851838}{43} n = - \frac{1851838}{43}

Solution

n_{1} = - \frac{1851838}{43}, n_{2} = \frac{1851838}{43}

Alternative Form

n_{1} \approx - 31.647036, n_{2} \approx 31.647036

Show Solution