Basic Math Examples

$0.26 y + 0.052 = y^{2} - 0.6 y + 9$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$y^{2} - 0.6 y + 9 = 0.26 y + 0.052$

Step 2

Move all terms containing $y$ to the left side of the equation.

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Step 2.1

Subtract $0.26 y$ from both sides of the equation.

$y^{2} - 0.6 y + 9 - 0.26 y = 0.052$

Step 2.2

Subtract $0.26 y$ from $- 0.6 y$ .

$y^{2} - 0.86 y + 9 = 0.052$

Step 3

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

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Step 3.1

Subtract $0.052$ from both sides of the equation.

$y^{2} - 0.86 y + 9 - 0.052 = 0$

Step 3.2

Subtract $0.052$ from $9$ .

$y^{2} - 0.86 y + 8.948 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 1$ , $b = - 0.86$ , and $c = 8.948$ into the quadratic formula and solve for $y$ .

$\frac{0.86 \pm \sqrt{{(- 0.86)}^{2} - 4 \cdot (1 \cdot 8.948)}}{2 \cdot 1}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $- 0.86$ to the power of $2$ .

$y = \frac{0.86 \pm \sqrt{0.7396 - 4 \cdot 1 \cdot 8.948}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4 \cdot 1 \cdot 8.948$ .

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Step 6.1.2.1

Multiply $- 4$ by $1$ .

$y = \frac{0.86 \pm \sqrt{0.7396 - 4 \cdot 8.948}}{2 \cdot 1}$

Step 6.1.2.2

Multiply $- 4$ by $8.948$ .

$y = \frac{0.86 \pm \sqrt{0.7396 - 35.792}}{2 \cdot 1}$

Step 6.1.3

Subtract $35.792$ from $0.7396$ .

$y = \frac{0.86 \pm \sqrt{- 35.0524}}{2 \cdot 1}$

Step 6.1.4

Rewrite $- 35.0524$ as $- 1 (35.0524)$ .

$y = \frac{0.86 \pm \sqrt{- 1 \cdot 35.0524}}{2 \cdot 1}$

Step 6.1.5

Rewrite $\sqrt{- 1 (35.0524)}$ as $\sqrt{- 1} \cdot \sqrt{35.0524}$ .

$y = \frac{0.86 \pm \sqrt{- 1} \cdot \sqrt{35.0524}}{2 \cdot 1}$

Step 6.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \frac{0.86 \pm i \sqrt{35.0524}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$y = \frac{0.86 \pm i \sqrt{35.0524}}{2}$

Step 7

The final answer is the combination of both solutions.

$y = \frac{0.86 + i \sqrt{35.0524}}{2}, \frac{0.86 - i \sqrt{35.0524}}{2}$