Solve x^2/49+25-x^2/24=1

$$\frac{ { x }^{ 2 } }{ 49 } + \frac{ 25- { x }^{ 2 } }{ 24 } =1$$

Solve for x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

$$x = -\frac{7}{5} = -1\frac{2}{5} = -1.4$$

Steps by Finding Square Root

Multiply both sides of the equation by 1176, the least common multiple of 49,24.

$$24x^{2}+49\left(25-x^{2}\right)=1176$$

Use the distributive property to multiply 49 by 25-x^{2}.

$$24x^{2}+1225-49x^{2}=1176$$

Combine 24x^{2} and -49x^{2} to get -25x^{2}.

$$-25x^{2}+1225=1176$$

Subtract 1225 from both sides.

$$-25x^{2}=1176-1225$$

Subtract 1225 from 1176 to get -49.

$$-25x^{2}=-49$$

Divide both sides by -25.

$$x^{2}=\frac{-49}{-25}$$

Fraction \frac{-49}{-25} can be simplified to \frac{49}{25} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{49}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{5} x=-\frac{7}{5}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 1176, the least common multiple of 49,24.

$$24x^{2}+49\left(25-x^{2}\right)=1176$$

Use the distributive property to multiply 49 by 25-x^{2}.

$$24x^{2}+1225-49x^{2}=1176$$

Combine 24x^{2} and -49x^{2} to get -25x^{2}.

$$-25x^{2}+1225=1176$$

Subtract 1176 from both sides.

$$-25x^{2}[phone]=0$$

Subtract 1176 from 1225 to get 49.

$$-25x^{2}+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -25 for a, 0 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25\right)\times 49}}{2\left(-25\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-25\right)\times 49}}{2\left(-25\right)}$$

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100\times 49}}{2\left(-25\right)}$$

Multiply 100 times 49.

$$x=\frac{0±\sqrt{4900}}{2\left(-25\right)}$$

Take the square root of 4900.

$$x=\frac{0±70}{2\left(-25\right)}$$

Multiply 2 times -25.

$$x=\frac{0±70}{-50}$$

Now solve the equation x=\frac{0±70}{-50} when ± is plus. Reduce the fraction \frac{70}{-50} to lowest terms by extracting and canceling out 10.

$$x=-\frac{7}{5}$$

Now solve the equation x=\frac{0±70}{-50} when ± is minus. Reduce the fraction \frac{-70}{-50} to lowest terms by extracting and canceling out 10.

$$x=\frac{7}{5}$$

The equation is now solved.

$$x=-\frac{7}{5} x=\frac{7}{5}$$