Solve 9x^2+4x^2=2*9.5^2+2*8.5^2

$$9 { x }^{ 2 } +4 { x }^{ 2 } =2 \times { 9.5 }^{ 2 } +2 \times { 8.5 }^{ 2 }$$

Solve for x

$$x=5$$

$$x=-5$$

Steps Using Difference of Squares

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}=2\times 9.5^{2}+2\times 8.5^{2}$$

Calculate 9.5 to the power of 2 and get 90.25.

$$13x^{2}=2\times 90.25+2\times 8.5^{2}$$

Multiply 2 and 90.25 to get 180.5.

$$13x^{2}=180.5+2\times 8.5^{2}$$

Calculate 8.5 to the power of 2 and get 72.25.

$$13x^{2}=180.5+2\times 72.25$$

Multiply 2 and 72.25 to get 144.5.

$$13x^{2}=180.5+144.5$$

Add 180.5 and 144.5 to get 325.

$$13x^{2}=325$$

Subtract 325 from both sides.

$$13x^{2}-325=0$$

Divide both sides by 13.

$$x^{2}-25=0$$

Consider x^{2}-25. Rewrite x^{2}-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

To find equation solutions, solve x-5=0 and x+5=0.

$$x=5 x=-5$$

Steps by Finding Square Root

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}=2\times 9.5^{2}+2\times 8.5^{2}$$

Calculate 9.5 to the power of 2 and get 90.25.

$$13x^{2}=2\times 90.25+2\times 8.5^{2}$$

Multiply 2 and 90.25 to get 180.5.

$$13x^{2}=180.5+2\times 8.5^{2}$$

Calculate 8.5 to the power of 2 and get 72.25.

$$13x^{2}=180.5+2\times 72.25$$

Multiply 2 and 72.25 to get 144.5.

$$13x^{2}=180.5+144.5$$

Add 180.5 and 144.5 to get 325.

$$13x^{2}=325$$

Divide both sides by 13.

$$x^{2}=\frac{325}{13}$$

Divide 325 by 13 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}=2\times 9.5^{2}+2\times 8.5^{2}$$

Calculate 9.5 to the power of 2 and get 90.25.

$$13x^{2}=2\times 90.25+2\times 8.5^{2}$$

Multiply 2 and 90.25 to get 180.5.

$$13x^{2}=180.5+2\times 8.5^{2}$$

Calculate 8.5 to the power of 2 and get 72.25.

$$13x^{2}=180.5+2\times 72.25$$

Multiply 2 and 72.25 to get 144.5.

$$13x^{2}=180.5+144.5$$

Add 180.5 and 144.5 to get 325.

$$13x^{2}=325$$

Subtract 325 from both sides.

$$13x^{2}-325=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -325 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-325\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-325\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-325\right)}}{2\times 13}$$

Multiply -52 times -325.

$$x=\frac{0±\sqrt{16900}}{2\times 13}$$

Take the square root of 16900.

$$x=\frac{0±130}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±130}{26}$$

Now solve the equation x=\frac{0±130}{26} when ± is plus. Divide 130 by 26.

$$x=5$$

Now solve the equation x=\frac{0±130}{26} when ± is minus. Divide -130 by 26.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$