Solve -7x^2+343=0

$$- 7 x ^ { 2 } + 343 = 0$$

Solve for x

$$x=7$$

$$x=-7$$

Steps by Finding Square Root

Subtract 343 from both sides. Anything subtracted from zero gives its negation.

$$-7x^{2}=-343$$

Divide both sides by -7.

$$x^{2}=\frac{-343}{-7}$$

Divide -343 by -7 to get 49.

$$x^{2}=49$$

Take the square root of both sides of the equation.

$$x=7 x=-7$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-7x^{2}+343=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 343 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 343}}{2\left(-7\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-7\right)\times 343}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$x=\frac{0±\sqrt{28\times 343}}{2\left(-7\right)}$$

Multiply 28 times 343.

$$x=\frac{0±\sqrt{9604}}{2\left(-7\right)}$$

Take the square root of 9604.

$$x=\frac{0±98}{2\left(-7\right)}$$

Multiply 2 times -7.

$$x=\frac{0±98}{-14}$$

Now solve the equation x=\frac{0±98}{-14} when ± is plus. Divide 98 by -14.

$$x=-7$$

Now solve the equation x=\frac{0±98}{-14} when ± is minus. Divide -98 by -14.

$$x=7$$

The equation is now solved.

$$x=-7 x=7$$