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Popular >

solvefor y,d^2-4d+4y=e^2x+x^2+x+sin^2(x)

Solution

solve for

y, d^{2} - 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x)

Solution

y = \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

Solution steps

d^{2} - 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x)

Move

d^{2}

to the right side

d^{2} - 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x)

Subtract

d^{2}

from both sides

d^{2} - 4 d + 4 y - d^{2} = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2}

Simplify

- 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2}

- 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2}

Move

4 d

to the right side

- 4 d + 4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2}

Add

4 d

to both sides

- 4 d + 4 y + 4 d = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2} + 4 d

Simplify

4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2} + 4 d

4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2} + 4 d

Divide both sides by

4

4 y = e^{2} x + x^{2} + x + sin^{2} (x) - d^{2} + 4 d

Divide both sides by

4

\frac{4 y}{4} = \frac{e ^{2} x}{4} + \frac{x ^{2}}{4} + \frac{x}{4} + \frac{sin ^{2} ( x )}{4} - \frac{d ^{2}}{4} + \frac{4 d}{4}

Simplify

\frac{4 y}{4} = \frac{e ^{2} x}{4} + \frac{x ^{2}}{4} + \frac{x}{4} + \frac{sin ^{2} ( x )}{4} - \frac{d ^{2}}{4} + \frac{4 d}{4}

Simplify

\frac{4 y}{4} : y

\frac{4 y}{4}

Divide the numbers:

\frac{4}{4} = 1

= y

Simplify

\frac{e ^{2} x}{4} + \frac{x ^{2}}{4} + \frac{x}{4} + \frac{sin ^{2} ( x )}{4} - \frac{d ^{2}}{4} + \frac{4 d}{4} : \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

\frac{e ^{2} x}{4} + \frac{x ^{2}}{4} + \frac{x}{4} + \frac{sin ^{2} ( x )}{4} - \frac{d ^{2}}{4} + \frac{4 d}{4}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

y = \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

y = \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

y = \frac{e ^{2} x + x ^{2} + x + sin ^{2} ( x ) - d ^{2} + 4 d}{4}

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