Calculus Examples

$4 \sqrt{0.5 x + 4} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1

Simplify $4 \sqrt{0.5 x + 4} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $0.5$ out of $0.5 x + 4$ .

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Step 1.1.1.1

Factor $0.5$ out of $0.5 x$ .

$4 \sqrt{0.5 (x) + 4} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.1.2

Factor $0.5$ out of $4$ .

$4 \sqrt{0.5 x + 0.5 \cdot 8} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.1.3

Factor $0.5$ out of $0.5 x + 0.5 \cdot 8$ .

$4 \sqrt{0.5 (x + 8)} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.2

Rewrite $0.5 (x + 8)$ as ${({0.84089641}^{2})}^{2} (x + 8)$ .

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Step 1.1.2.1

Rewrite $0.5$ as ${0.70710678}^{2}$ .

$4 \sqrt{{0.70710678}^{2} (x + 8)} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.2.2

Rewrite $0.70710678$ as ${0.84089641}^{2}$ .

$4 \sqrt{{({0.84089641}^{2})}^{2} (x + 8)} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.3

Pull terms out from under the radical.

$4 ({0.84089641}^{2} \sqrt{x + 8}) + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.4

Raise $0.84089641$ to the power of $2$ .

$4 (0.70710678 \sqrt{x + 8}) + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.1.5

Multiply $0.70710678$ by $4$ .

$2.82842712 \sqrt{x + 8} + 2.8 x - 8 + 33.365 - {(x + 180)}^{1.05} = 0$

Step 1.2

Add $- 8$ and $33.365$ .

$2.82842712 \sqrt{x + 8} + 2.8 x + 25.365 - {(x + 180)}^{1.05} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution