Solve -10+frac{sqrt{10^2-4(-4.8)(25)}}{2(-4.8)}

$$-10+ \frac{ \sqrt{ { 10 }^{ 2 } -4(-4.8)(25) } }{ 2(-4.8) }$$

Evaluate

$$-\frac{5\sqrt{145}}{24}-10\approx -12.508665537$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$-10+\frac{\sqrt{100-4\left(-4.8\right)\times 25}}{2\left(-4.8\right)}$$

Multiply 4 and -4.8 to get -19.2.

$$-10+\frac{\sqrt{100-\left(-19.2\times 25\right)}}{2\left(-4.8\right)}$$

Multiply -19.2 and 25 to get -480.

$$-10+\frac{\sqrt{100-\left(-480\right)}}{2\left(-4.8\right)}$$

The opposite of -480 is 480.

$$-10+\frac{\sqrt{100+480}}{2\left(-4.8\right)}$$

Add 100 and 480 to get 580.

$$-10+\frac{\sqrt{580}}{2\left(-4.8\right)}$$

Factor 580=2^{2}\times 145. Rewrite the square root of the product \sqrt{2^{2}\times 145} as the product of square roots \sqrt{2^{2}}\sqrt{145}. Take the square root of 2^{2}.

$$-10+\frac{2\sqrt{145}}{2\left(-4.8\right)}$$

Multiply 2 and -4.8 to get -9.6.

$$-10+\frac{2\sqrt{145}}{-9.6}$$

Divide 2\sqrt{145} by -9.6 to get -\frac{5}{24}\sqrt{145}.

$$-10-\frac{5}{24}\sqrt{145}$$

Factor

$$\frac{5 {(-\sqrt{145} - 48)}}{24} = -12.508665537248396$$