Solve 2.9+3.3*2+3.6*3+4.4*4+4.8*5+5.2*6+5.9*7-7*4*4.3/left(2.9-4right)^2+left(3.3-4right)^2+left(3.6-4right)^2+0.4^2+{0.8^2+{1.2}^2+{1.9}^2}

$$\frac{ 2.9+3.3 \times 2+3.6 \times 3+4.4 \times 4+4.8 \times 5+5.2 \times 6+5.9 \times 7-7 \times 4 \times 4.3 }{ { \left(2.9-4 \right) }^{ 2 } + { \left(3.3-4 \right) }^{ 2 } + { \left(3.6-4 \right) }^{ 2 } + { 0.4 }^{ 2 } + { 0.8 }^{ 2 } + { 1.2 }^{ 2 } + { 1.9 }^{ 2 } }$$

Evaluate

$$\frac{1400}{771}\approx 1.815823606$$

Solution Steps

Multiply 3.3 and 2 to get 6.6.

$$\frac{2.9+6.6+3.6\times 3+4.4\times 4+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 2.9 and 6.6 to get 9.5.

$$\frac{9.5+3.6\times 3+4.4\times 4+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 3.6 and 3 to get 10.8.

$$\frac{9.5+10.8+4.4\times 4+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 9.5 and 10.8 to get 20.3.

$$\frac{20.3+4.4\times 4+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 4.4 and 4 to get 17.6.

$$\frac{20.3+17.6+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 20.3 and 17.6 to get 37.9.

$$\frac{37.9+4.8\times 5+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 4.8 and 5 to get 24.

$$\frac{37.9+24+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 37.9 and 24 to get 61.9.

$$\frac{61.9+5.2\times 6+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 5.2 and 6 to get 31.2.

$$\frac{61.9+31.2+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 61.9 and 31.2 to get 93.1.

$$\frac{93.1+5.9\times 7-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 5.9 and 7 to get 41.3.

$$\frac{93.1+41.3-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 93.1 and 41.3 to get 134.4.

$$\frac{134.4-7\times 4\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 7 and 4 to get 28.

$$\frac{134.4-28\times 4.3}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Multiply 28 and 4.3 to get 120.4.

$$\frac{134.4-120.4}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Subtract 120.4 from 134.4 to get 14.

$$\frac{14}{\left(2.9-4\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Subtract 4 from 2.9 to get -1.1.

$$\frac{14}{\left(-1.1\right)^{2}+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Calculate -1.1 to the power of 2 and get 1.21.

$$\frac{14}{1.21+\left(3.3-4\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Subtract 4 from 3.3 to get -0.7.

$$\frac{14}{1.21+\left(-0.7\right)^{2}+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Calculate -0.7 to the power of 2 and get 0.49.

$$\frac{14}{1.21+0.49+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 1.21 and 0.49 to get 1.7.

$$\frac{14}{1.7+\left(3.6-4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Subtract 4 from 3.6 to get -0.4.

$$\frac{14}{1.7+\left(-0.4\right)^{2}+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Calculate -0.4 to the power of 2 and get 0.16.

$$\frac{14}{1.7+0.16+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 1.7 and 0.16 to get 1.86.

$$\frac{14}{1.86+0.4^{2}+0.8^{2}+1.2^{2}+1.9^{2}}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$\frac{14}{1.86+0.16+0.8^{2}+1.2^{2}+1.9^{2}}$$

Add 1.86 and 0.16 to get 2.02.

$$\frac{14}{2.02+0.8^{2}+1.2^{2}+1.9^{2}}$$

Calculate 0.8 to the power of 2 and get 0.64.

$$\frac{14}{2.02+0.64+1.2^{2}+1.9^{2}}$$

Add 2.02 and 0.64 to get 2.66.

$$\frac{14}{2.66+1.2^{2}+1.9^{2}}$$

Calculate 1.2 to the power of 2 and get 1.44.

$$\frac{14}{2.66+1.44+1.9^{2}}$$

Add 2.66 and 1.44 to get 4.1.

$$\frac{14}{4.1+1.9^{2}}$$

Calculate 1.9 to the power of 2 and get 3.61.

$$\frac{14}{4.1+3.61}$$

Add 4.1 and 3.61 to get 7.71.

$$\frac{14}{7.71}$$

Expand \frac{14}{7.71} by multiplying both numerator and the denominator by 100.

$$\frac{1400}{771}$$

Factor

$$\frac{7 \cdot 2 ^ {3} \cdot 5 ^ {2}}{3 \cdot 257} = 1\frac{629}{771} = 1.8158236057068742$$