Solve r^2+(5.951*10^20)r-3*10^42=0

$$r ^ { 2 } + ( 5.951 \times 10 ^ { 20 } ) r - 3 \times 10 ^ { 42 } = 0$$

Solve for r

$$r=50000000000000000\sqrt{1235414401}-297550000000000000000\approx 1.459873114 \cdot 10^{21}$$

$$r=-50000000000000000\sqrt{1235414401}-297550000000000000000\approx -2.054973114 \cdot 10^{21}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 20 and get 100000000000000000000.

$$r^{2}+5.951\times 100000000000000000000r-3\times 10^{42}=0$$

Multiply 5.951 and 100000000000000000000 to get 595100000000000000000.

$$r^{2}+595100000000000000000r-3\times 10^{42}=0$$

Calculate 10 to the power of 42 and get 1000000000000000000000000000000000000000000.

$$r^{2}+595100000000000000000r-3\times 1000000000000000000000000000000000000000000=0$$

Multiply 3 and 1000000000000000000000000000000000000000000 to get 3000000000000000000000000000000000000000000.

$$r^{2}+595100000000000000000r-3000000000000000000000000000000000000000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 595100000000000000000 for b, and -3000000000000000000000000000000000000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{-595100000000000000000±\sqrt{595100000000000000000^{2}-4\left(-3000000000000000000000000000000000000000000\right)}}{2}$$

Square 595100000000000000000.

$$r=\frac{-595100000000000000000±\sqrt{354144010000000000000000000000000000000000-4\left(-3000000000000000000000000000000000000000000\right)}}{2}$$

Multiply -4 times -3000000000000000000000000000000000000000000.

$$r=\frac{-595100000000000000000±\sqrt{354144010000000000000000000000000000000000+12000000000000000000000000000000000000000000}}{2}$$

Add 354144010000000000000000000000000000000000 to 12000000000000000000000000000000000000000000.

$$r=\frac{-595100000000000000000±\sqrt{12354144010000000000000000000000000000000000}}{2}$$

Take the square root of 12354144010000000000000000000000000000000000.

$$r=\frac{-595100000000000000000±100000000000000000\sqrt{1235414401}}{2}$$

Now solve the equation r=\frac{-595100000000000000000±100000000000000000\sqrt{1235414401}}{2} when ± is plus. Add -595100000000000000000 to 100000000000000000\sqrt{1235414401}.

$$r=\frac{100000000000000000\sqrt{1235414401}-595100000000000000000}{2}$$

Divide -595100000000000000000+100000000000000000\sqrt{1235414401} by 2.

$$r=50000000000000000\sqrt{1235414401}-297550000000000000000$$

Now solve the equation r=\frac{-595100000000000000000±100000000000000000\sqrt{1235414401}}{2} when ± is minus. Subtract 100000000000000000\sqrt{1235414401} from -595100000000000000000.

$$r=\frac{-100000000000000000\sqrt{1235414401}-595100000000000000000}{2}$$

Divide -595100000000000000000-100000000000000000\sqrt{1235414401} by 2.

$$r=-50000000000000000\sqrt{1235414401}-297550000000000000000$$

The equation is now solved.

$$r=50000000000000000\sqrt{1235414401}-297550000000000000000 r=-50000000000000000\sqrt{1235414401}-297550000000000000000$$

Steps for Completing the Square

Calculate 10 to the power of 20 and get 100000000000000000000.

$$r^{2}+5.951\times 100000000000000000000r-3\times 10^{42}=0$$

Multiply 5.951 and 100000000000000000000 to get 595100000000000000000.

$$r^{2}+595100000000000000000r-3\times 10^{42}=0$$

Calculate 10 to the power of 42 and get 1000000000000000000000000000000000000000000.

$$r^{2}+595100000000000000000r-3\times 1000000000000000000000000000000000000000000=0$$

Multiply 3 and 1000000000000000000000000000000000000000000 to get 3000000000000000000000000000000000000000000.

$$r^{2}+595100000000000000000r-3000000000000000000000000000000000000000000=0$$

Add 3000000000000000000000000000000000000000000 to both sides. Anything plus zero gives itself.

$$r^{2}+595100000000000000000r=3000000000000000000000000000000000000000000$$

Divide 595100000000000000000, the coefficient of the x term, by 2 to get 297550000000000000000. Then add the square of 297550000000000000000 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$r^{2}+595100000000000000000r+297550000000000000000^{2}=3000000000000000000000000000000000000000000+297550000000000000000^{2}$$

Square 297550000000000000000.

$$r^{2}+595100000000000000000r+88536002500000000000000000000000000000000=3000000000000000000000000000000000000000000+88536002500000000000000000000000000000000$$

Add 3000000000000000000000000000000000000000000 to 88536002500000000000000000000000000000000.

$$r^{2}+595100000000000000000r+88536002500000000000000000000000000000000=3088536002500000000000000000000000000000000$$

Factor r^{2}+595100000000000000000r+88536002500000000000000000000000000000000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(r+297550000000000000000\right)^{2}=3088536002500000000000000000000000000000000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(r+297550000000000000000\right)^{2}}=\sqrt{3088536002500000000000000000000000000000000}$$

Simplify.

$$r+297550000000000000000=50000000000000000\sqrt{1235414401} r+297550000000000000000=-50000000000000000\sqrt{1235414401}$$

Subtract 297550000000000000000 from both sides of the equation.

$$r=50000000000000000\sqrt{1235414401}-297550000000000000000 r=-50000000000000000\sqrt{1235414401}-297550000000000000000$$