Finite Math Examples

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

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

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Step 1.1.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1.1.2.1

Move $y$ .

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

Step 1.1.1.2.2

Multiply $y$ by $y$ .

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

Step 1.1.1.3

Multiply $- 5.1$ by $7.2$ .

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

Step 1.2

Add $8.4$ to both sides of the equation.

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

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = - 36.72$ , $b = 0$ , and $c = 8.4$ into the quadratic formula and solve for $y$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

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

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $- 36.72$ .

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

Step 4.1.2.2

Multiply $146.88$ by $8.4$ .

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

Step 4.1.3

Add $0$ and $1233.792$ .

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

Step 4.2

Multiply $2$ by $- 36.72$ .

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

Step 4.3

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

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

Step 4.4

Multiply by $1$ .

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

Step 4.5

Factor $73.44$ out of $73.44$ .

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

Step 4.6

Separate fractions.

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

Step 4.7

Divide $1$ by $73.44$ .

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

Step 4.8

Divide $\pm \sqrt{1233.792}$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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