Solve a^{2}=[36*sin14^{circ}+(26-30*cos52^{circ})]^2+[36cos14^circ+30sin52^circ]^2

$$a ^ { 2 } = [ 36 \times \sin 14 ^ { \circ } + ( 26 - 30 \times \cos 52 ^ { \circ } ) ] ^ { 2 } + [ 36 \cos 14 ^ { \circ } + 30 \sin 52 ^ { \circ } ] ^ { 2 }$$

Solve for a

$$a = \frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000} = 60\frac{9756814891899008}{12500000000000000} \approx 60.780545191$$

$$a = -\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000} = -60\frac{9756814891899008}{12500000000000000} \approx -60.780545191$$

Steps by Finding Square Root

Evaluate trigonometric functions in the problem

$$a ^ {2} = {(36 \cdot 0.24192189559966773 + {(26 - 30 \cdot 0.6156614753256583)})} ^ {2} + {(36 \cdot 0.9702957262759965 + 30 \cdot 0.788010753606722)} ^ {2}$$

Multiply 36 and 0.24192189559966773 to get 8.70918824158803828.

$$a^{2}=\left(8.70918824158803828+26-30\times 0.6156614753256583\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Multiply 30 and 0.6156614753256583 to get 18.469844259769749.

$$a^{2}=\left(8.70918824158803828+26-18.469844259769749\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Subtract 18.469844259769749 from 26 to get 7.530155740230251.

$$a^{2}=\left(8.70918824158803828+7.530155740230251\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Add 8.70918824158803828 and 7.530155740230251 to get 16.23934398181828928.

$$a^{2}=16.23934398181828928^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Calculate 16.23934398181828928 to the power of 2 and get 263.7162929598178905494392447057629184.

$$a^{2}=263.7162929598178905494392447057629184+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Multiply 36 and 0.9702957262759965 to get 34.930646145935874.

$$a^{2}=263.7162929598178905494392447057629184+\left(34.930646145935874+30\times 0.788010753606722\right)^{2}$$

Multiply 30 and 0.788010753606722 to get 23.64032260820166.

$$a^{2}=263.7162929598178905494392447057629184+\left(34.930646145935874+23.64032260820166\right)^{2}$$

Add 34.930646145935874 and 23.64032260820166 to get 58.570968754137534.

$$a^{2}=263.7162929598178905494392447057629184+58.570968754137534^{2}$$

Calculate 58.570968754137534 to the power of 2 and get 3430.558380798155311749244187601156.

$$a^{2}=263.7162929598178905494392447057629184+3430.558380798155311749244187601156$$

Add 263.7162929598178905494392447057629184 and 3430.558380798155311749244187601156 to get 3694.2746737579732022986834323069189184.

$$a^{2}=3694.2746737579732022986834323069189184$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000} a=-\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000}$$

Steps Using the Quadratic Formula

Evaluate trigonometric functions in the problem

$$a ^ {2} = {(36 \cdot 0.24192189559966773 + {(26 - 30 \cdot 0.6156614753256583)})} ^ {2} + {(36 \cdot 0.9702957262759965 + 30 \cdot 0.788010753606722)} ^ {2}$$

Multiply 36 and 0.24192189559966773 to get 8.70918824158803828.

$$a^{2}=\left(8.70918824158803828+26-30\times 0.6156614753256583\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Multiply 30 and 0.6156614753256583 to get 18.469844259769749.

$$a^{2}=\left(8.70918824158803828+26-18.469844259769749\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Subtract 18.469844259769749 from 26 to get 7.530155740230251.

$$a^{2}=\left(8.70918824158803828+7.530155740230251\right)^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Add 8.70918824158803828 and 7.530155740230251 to get 16.23934398181828928.

$$a^{2}=16.23934398181828928^{2}+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Calculate 16.23934398181828928 to the power of 2 and get 263.7162929598178905494392447057629184.

$$a^{2}=263.7162929598178905494392447057629184+\left(36\times 0.9702957262759965+30\times 0.788010753606722\right)^{2}$$

Multiply 36 and 0.9702957262759965 to get 34.930646145935874.

$$a^{2}=263.7162929598178905494392447057629184+\left(34.930646145935874+30\times 0.788010753606722\right)^{2}$$

Multiply 30 and 0.788010753606722 to get 23.64032260820166.

$$a^{2}=263.7162929598178905494392447057629184+\left(34.930646145935874+23.64032260820166\right)^{2}$$

Add 34.930646145935874 and 23.64032260820166 to get 58.570968754137534.

$$a^{2}=263.7162929598178905494392447057629184+58.570968754137534^{2}$$

Calculate 58.570968754137534 to the power of 2 and get 3430.558380798155311749244187601156.

$$a^{2}=263.7162929598178905494392447057629184+3430.558380798155311749244187601156$$

Add 263.7162929598178905494392447057629184 and 3430.558380798155311749244187601156 to get 3694.2746737579732022986834323069189184.

$$a^{2}=3694.2746737579732022986834323069189184$$

Subtract 3694.2746737579732022986834323069189184 from both sides.

$$a^{2}-3694.2746737579732022986834323069189184=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3694.2746737579732022986834323069189184 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-3694.2746737579732022986834323069189184\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-3694.2746737579732022986834323069189184\right)}}{2}$$

Multiply -4 times -3694.2746737579732022986834323069189184.

$$a=\frac{0±\sqrt{14777.0986950318928091947337292276756736}}{2}$$

Take the square root of 14777.0986950318928091947337292276756736.

$$a=\frac{0±\frac{\sqrt{577230417774683312859169286297956081}}{6250000000000000}}{2}$$

Now solve the equation a=\frac{0±\frac{\sqrt{577230417774683312859169286297956081}}{6250000000000000}}{2} when ± is plus.

$$a=\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000}$$

Now solve the equation a=\frac{0±\frac{\sqrt{577230417774683312859169286297956081}}{6250000000000000}}{2} when ± is minus.

$$a=-\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000}$$

The equation is now solved.

$$a=\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000} a=-\frac{\sqrt{577230417774683312859169286297956081}}{12500000000000000}$$