Solve 1x^2+2+3+4+5+6+7+8+9=155

$$1 { x }^{ 2 } +2+3+4+5+6+7+8+9 = 155$$

Solve for x

$$x=\sqrt{111}\approx 10.535653753$$

$$x=-\sqrt{111}\approx -10.535653753$$

Steps by Finding Square Root

Add 2 and 3 to get 5.

$$1x^{2}+5+4+5+6+7+8+9=155$$

Add 5 and 4 to get 9.

$$1x^{2}+9+5+6+7+8+9=155$$

Add 9 and 5 to get 14.

$$1x^{2}+14+6+7+8+9=155$$

Add 14 and 6 to get 20.

$$1x^{2}+20+7+8+9=155$$

Add 20 and 7 to get 27.

$$1x^{2}+27+8+9=155$$

Add 27 and 8 to get 35.

$$1x^{2}+35+9=155$$

Add 35 and 9 to get 44.

$$1x^{2}+44=155$$

Subtract 44 from both sides.

$$1x^{2}=155-44$$

Subtract 44 from 155 to get 111.

$$1x^{2}=111$$

Divide both sides by 1.

$$x^{2}=111$$

Take the square root of both sides of the equation.

$$x=\sqrt{111} x=-\sqrt{111}$$

Steps Using the Quadratic Formula

Add 2 and 3 to get 5.

$$1x^{2}+5+4+5+6+7+8+9=155$$

Add 5 and 4 to get 9.

$$1x^{2}+9+5+6+7+8+9=155$$

Add 9 and 5 to get 14.

$$1x^{2}+14+6+7+8+9=155$$

Add 14 and 6 to get 20.

$$1x^{2}+20+7+8+9=155$$

Add 20 and 7 to get 27.

$$1x^{2}+27+8+9=155$$

Add 27 and 8 to get 35.

$$1x^{2}+35+9=155$$

Add 35 and 9 to get 44.

$$1x^{2}+44=155$$

Subtract 155 from both sides.

$$1x^{2}+44-155=0$$

Subtract 155 from 44 to get -111.

$$1x^{2}-111=0$$

Reorder the terms.

$$x^{2}-111=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -111 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-111\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-111\right)}}{2}$$

Multiply -4 times -111.

$$x=\frac{0±\sqrt{444}}{2}$$

Take the square root of 444.

$$x=\frac{0±2\sqrt{111}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{111}}{2} when ± is plus.

$$x=\sqrt{111}$$

Now solve the equation x=\frac{0±2\sqrt{111}}{2} when ± is minus.

$$x=-\sqrt{111}$$

The equation is now solved.

$$x=\sqrt{111} x=-\sqrt{111}$$