Trigonometry Examples

$10 x^{2} - 10 x = 4 x^{2} - 3 x + 10$

Step 1

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

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Step 1.1

Move all the expressions to the left side of the equation.

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Step 1.1.1

Subtract $4 x^{2}$ from both sides of the equation.

$10 x^{2} - 10 x - 4 x^{2} = - 3 x + 10$

Step 1.1.2

Add $3 x$ to both sides of the equation.

$10 x^{2} - 10 x - 4 x^{2} + 3 x = 10$

Step 1.1.3

Subtract $10$ from both sides of the equation.

$10 x^{2} - 10 x - 4 x^{2} + 3 x - 10 = 0$

Step 1.2

Simplify $10 x^{2} - 10 x - 4 x^{2} + 3 x - 10$ .

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Step 1.2.1

Subtract $4 x^{2}$ from $10 x^{2}$ .

$6 x^{2} - 10 x + 3 x - 10 = 0$

Step 1.2.2

Add $- 10 x$ and $3 x$ .

$6 x^{2} - 7 x - 10 = 0$

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 $a = 6$ , $b = - 7$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (6 \cdot - 10)}}{2 \cdot 6}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 6 \cdot - 10}}{2 \cdot 6}$

Step 4.1.2

Multiply $- 4 \cdot 6 \cdot - 10$ .

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Step 4.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{7 \pm \sqrt{49 - 24 \cdot - 10}}{2 \cdot 6}$

Step 4.1.2.2

Multiply $- 24$ by $- 10$ .

$x = \frac{7 \pm \sqrt{49 + 240}}{2 \cdot 6}$

Step 4.1.3

Add $49$ and $240$ .

$x = \frac{7 \pm \sqrt{289}}{2 \cdot 6}$

Step 4.1.4

Rewrite $289$ as $17^{2}$ .

$x = \frac{7 \pm \sqrt{17^{2}}}{2 \cdot 6}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{7 \pm 17}{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$x = \frac{7 \pm 17}{12}$

Step 5

The final answer is the combination of both solutions.

$x = 2, - \frac{5}{6}$