Finite Math Examples

- 5.1 y \cdot (7.2 y) = - 8.4

$- 5.1 y \cdot (7.2 y) = - 8.4$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify

- 5.1 y \cdot (7.2 y)

$- 5.1 y \cdot (7.2 y)$ .

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Step 1.1.1.1

Rewrite using the commutative property of multiplication.

- 5.1 \cdot 7.2 y \cdot y = - 8.4

$- 5.1 \cdot 7.2 y \cdot y = - 8.4$

Step 1.1.1.2

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 1.1.1.2.1

Move

y

$y$ .

- 5.1 \cdot 7.2 (y \cdot y) = - 8.4

$- 5.1 \cdot 7.2 (y \cdot y) = - 8.4$

Step 1.1.1.2.2

Multiply

y

$y$ by

y

$y$ .

- 5.1 \cdot 7.2 y^{2} = - 8.4

$- 5.1 \cdot 7.2 y^{2} = - 8.4$

- 5.1 \cdot 7.2 y^{2} = - 8.4

$- 5.1 \cdot 7.2 y^{2} = - 8.4$

Step 1.1.1.3

Multiply

- 5.1

$- 5.1$ by

7.2

$7.2$ .

- 36.72 y^{2} = - 8.4

$- 36.72 y^{2} = - 8.4$

- 36.72 y^{2} = - 8.4

$- 36.72 y^{2} = - 8.4$

- 36.72 y^{2} = - 8.4

$- 36.72 y^{2} = - 8.4$

Step 1.2

Add

8.4

$8.4$ to both sides of the equation.

- 36.72 y^{2} + 8.4 = 0

$- 36.72 y^{2} + 8.4 = 0$

- 36.72 y^{2} + 8.4 = 0

$- 36.72 y^{2} + 8.4 = 0$

Step 2

Use the quadratic formula to find the solutions.

\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values

a = - 36.72

$a = - 36.72$ ,

b = 0

$b = 0$ , and

c = 8.4

$c = 8.4$ into the quadratic formula and solve for

y

$y$ .

\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 36.72 \cdot 8.4)}}{2 \cdot - 36.72}

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 36.72 \cdot 8.4)}}{2 \cdot - 36.72}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising

0

$0$ to any positive power yields

0

$0$ .

y = \frac{0 \pm \sqrt{0 - 4 \cdot - 36.72 \cdot 8.4}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{0 - 4 \cdot - 36.72 \cdot 8.4}}{2 \cdot - 36.72}$

Step 4.1.2

Multiply

- 4 \cdot - 36.72 \cdot 8.4

$- 4 \cdot - 36.72 \cdot 8.4$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

- 36.72

$- 36.72$ .

y = \frac{0 \pm \sqrt{0 + 146.88 \cdot 8.4}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{0 + 146.88 \cdot 8.4}}{2 \cdot - 36.72}$

Step 4.1.2.2

Multiply

146.88

$146.88$ by

8.4

$8.4$ .

y = \frac{0 \pm \sqrt{0 + 1233.792}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{0 + 1233.792}}{2 \cdot - 36.72}$

y = \frac{0 \pm \sqrt{0 + 1233.792}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{0 + 1233.792}}{2 \cdot - 36.72}$

Step 4.1.3

Add

0

$0$ and

1233.792

$1233.792$ .

y = \frac{0 \pm \sqrt{1233.792}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{1233.792}}{2 \cdot - 36.72}$

y = \frac{0 \pm \sqrt{1233.792}}{2 \cdot - 36.72}

$y = \frac{0 \pm \sqrt{1233.792}}{2 \cdot - 36.72}$

Step 4.2

Multiply

2

$2$ by

- 36.72

$- 36.72$ .

y = \frac{0 \pm \sqrt{1233.792}}{- 73.44}

$y = \frac{0 \pm \sqrt{1233.792}}{- 73.44}$

Step 4.3

Simplify

\frac{0 \pm \sqrt{1233.792}}{- 73.44}

$\frac{0 \pm \sqrt{1233.792}}{- 73.44}$ .

y = \frac{\pm \sqrt{1233.792}}{73.44}

$y = \frac{\pm \sqrt{1233.792}}{73.44}$

Step 4.4

Multiply by

1

$1$ .

y = \frac{1 (\pm \sqrt{1233.792})}{73.44}

$y = \frac{1 (\pm \sqrt{1233.792})}{73.44}$

Step 4.5

Factor

73.44

$73.44$ out of

73.44

$73.44$ .

y = \frac{1 (\pm \sqrt{1233.792})}{73.44 (1)}

$y = \frac{1 (\pm \sqrt{1233.792})}{73.44 (1)}$

Step 4.6

Separate fractions.

y = \frac{1}{73.44} \cdot \frac{\pm \sqrt{1233.792}}{1}

$y = \frac{1}{73.44} \cdot \frac{\pm \sqrt{1233.792}}{1}$

Step 4.7

Divide

1

$1$ by

73.44

$73.44$ .

y = 0.01361655 (\frac{\pm \sqrt{1233.792}}{1})

$y = 0.01361655 (\frac{\pm \sqrt{1233.792}}{1})$

Step 4.8

Divide

\pm \sqrt{1233.792}

$\pm \sqrt{1233.792}$ by

1

$1$ .

y = 0.01361655 (\pm \sqrt{1233.792})

$y = 0.01361655 (\pm \sqrt{1233.792})$

y = 0.01361655 (\pm \sqrt{1233.792})

$y = 0.01361655 (\pm \sqrt{1233.792})$

Step 5

The result can be shown in multiple forms.

Exact Form:

y = 0.01361655 (\pm \sqrt{1233.792})

$y = 0.01361655 (\pm \sqrt{1233.792})$

Decimal Form:

y = 0.47828670 \dots, - 0.47828670 \dots

$y = 0.47828670 \dots, - 0.47828670 \dots$