Solve x=left(10-14.22right)^2*.1+left(12-14.22right)^2*.3+left(14-14.22right)^2*.25+left(15-14.2right)^2*.14+{left(17-14.22right)}^2*0.6+{left(20-14.22right)}^2*.15

$$x= { \left(10-14.22 \right) }^{ 2 } \times .1+ { \left(12-14.22 \right) }^{ 2 } \times .3+ { \left(14-14.22 \right) }^{ 2 } \times .25+ { \left(15-14.2 \right) }^{ 2 } \times .14+ { \left(17-14.22 \right) }^{ 2 } \times 0.6+ { \left(20-14.22 \right) }^{ 2 } \times .15$$

Solve for x

$$x=13.00936$$

Steps for Solving Linear Equation

Subtract 14.22 from 10 to get -4.22.

$$x=\left(-4.22\right)^{2}\times 0.1+\left(12-14.22\right)^{2}\times 0.3+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Calculate -4.22 to the power of 2 and get 17.8084.

$$x=17.8084\times 0.1+\left(12-14.22\right)^{2}\times 0.3+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Multiply 17.8084 and 0.1 to get 1.78084.

$$x=1.78084+\left(12-14.22\right)^{2}\times 0.3+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Subtract 14.22 from 12 to get -2.22.

$$x=1.78084+\left(-2.22\right)^{2}\times 0.3+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Calculate -2.22 to the power of 2 and get 4.9284.

$$x=1.78084+4.9284\times 0.3+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Multiply 4.9284 and 0.3 to get 1.47852.

$$x=1.78084+1.47852+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Add 1.78084 and 1.47852 to get 3.25936.

$$x=3.25936+\left(14-14.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Subtract 14.22 from 14 to get -0.22.

$$x=3.25936+\left(-0.22\right)^{2}\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Calculate -0.22 to the power of 2 and get 0.0484.

$$x=3.25936+0.0484\times 0.25+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Multiply 0.0484 and 0.25 to get 0.0121.

$$x=3.25936+0.0121+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Add 3.25936 and 0.0121 to get 3.27146.

$$x=3.27146+\left(15-14.2\right)^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Subtract 14.2 from 15 to get 0.8.

$$x=3.27146+0.8^{2}\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Calculate 0.8 to the power of 2 and get 0.64.

$$x=3.27146+0.64\times 0.14+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Multiply 0.64 and 0.14 to get 0.0896.

$$x=3.27146+0.0896+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Add 3.27146 and 0.0896 to get 3.36106.

$$x=3.36106+\left(17-14.22\right)^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Subtract 14.22 from 17 to get 2.78.

$$x=3.36106+2.78^{2}\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Calculate 2.78 to the power of 2 and get 7.7284.

$$x=3.36106+7.7284\times 0.6+\left(20-14.22\right)^{2}\times 0.15$$

Multiply 7.7284 and 0.6 to get 4.63704.

$$x=3.36106+4.63704+\left(20-14.22\right)^{2}\times 0.15$$

Add 3.36106 and 4.63704 to get 7.9981.

$$x=7.9981+\left(20-14.22\right)^{2}\times 0.15$$

Subtract 14.22 from 20 to get 5.78.

$$x=7.9981+5.78^{2}\times 0.15$$

Calculate 5.78 to the power of 2 and get 33.4084.

$$x=7.9981+33.4084\times 0.15$$

Multiply 33.4084 and 0.15 to get 5.01126.

$$x=7.9981+5.01126$$

Add 7.9981 and 5.01126 to get 13.00936.

$$x=13.00936$$

Assign x

$$x≔13.00936$$