Solve 2025-w^22 - ScanMath

Question

Simplify the expression

2025 - 2 w^{2}

Evaluate

2025 - w^{2} \times 2

Solution

2025 - 2 w^{2}

Show Solution

w_{1} = - \frac{45 2}{2}, w_{2} = \frac{45 2}{2}

Alternative Form

w_{1} \approx - 31.819805, w_{2} \approx 31.819805

Evaluate

2025 - w^{2} \times 2

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

2025 - w^{2} \times 2 = 0

Use the commutative property to reorder the terms

2025 - 2 w^{2} = 0

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

- 2 w^{2} = 0 - 2025

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

- 2 w^{2} = - 2025

Change the signs on both sides of the equation

2 w^{2} = 2025

Divide both sides

\frac{2 w ^{2}}{2} = \frac{2025}{2}

Divide the numbers

w^{2} = \frac{2025}{2}

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

w = \pm \frac{2025}{2}

Simplify the expression

More Steps

Evaluate

\frac{2025}{2}

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

\frac{2025}{2}

Simplify the radical expression

More Steps

Evaluate

2025

Write the number in exponential form with the base of 45

4 5^{2}

Reduce the index of the radical and exponent with 2

45

\frac{45}{2}

Multiply by the Conjugate

\frac{45 2}{2 \times 2}

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

\frac{45 2}{2}

w = \pm \frac{45 2}{2}

Separate the equation into 2 possible cases

w = \frac{45 2}{2} w = - \frac{45 2}{2}

Solution

w_{1} = - \frac{45 2}{2}, w_{2} = \frac{45 2}{2}

Alternative Form

w_{1} \approx - 31.819805, w_{2} \approx 31.819805

Show Solution