Solve 2.0365*695x^2-34xdiv365=5874/65

$$2.0365 \times 695 { x }^{ 2 } -34x \div 365= \frac{ 5874 }{ 65 }$$

Solve for x

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}\approx 0.252715711$$

$$x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}\approx -0.252649897$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4745, the least common multiple of 365,65.

$$9663.1925\times 695x^{2}-13\times 34x=428802$$

Multiply 9663.1925 and 695 to get 6715918.7875.

$$6715918.7875x^{2}-13\times 34x=428802$$

Multiply -13 and 34 to get -442.

$$6715918.7875x^{2}-442x=428802$$

Subtract 428802 from both sides.

$$6715918.7875x^{2}-442x-428802=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6715918.7875 for a, -442 for b, and -428802 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-442\right)±\sqrt{\left(-442\right)^{2}-4\times 6715918.7875\left(-428802\right)}}{2\times 6715918.7875}$$

Square -442.

$$x=\frac{-\left(-442\right)±\sqrt{195364-4\times 6715918.7875\left(-428802\right)}}{2\times 6715918.7875}$$

Multiply -4 times 6715918.7875.

$$x=\frac{-\left(-442\right)±\sqrt{195364-26863675.15\left(-428802\right)}}{2\times 6715918.7875}$$

Multiply -26863675.15 times -428802.

$$x=\frac{-\left(-442\right)±\sqrt{195364+11519197631670.3}}{2\times 6715918.7875}$$

Add 195364 to 11519197631670.3.

$$x=\frac{-\left(-442\right)±\sqrt{11519197827034.3}}{2\times 6715918.7875}$$

Take the square root of 11519197827034.3.

$$x=\frac{-\left(-442\right)±\frac{\sqrt{1151919782703430}}{10}}{2\times 6715918.7875}$$

The opposite of -442 is 442.

$$x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{2\times 6715918.7875}$$

Multiply 2 times 6715918.7875.

$$x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575}$$

Now solve the equation x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575} when ± is plus. Add 442 to \frac{\sqrt{1151919782703430}}{10}.

$$x=\frac{\frac{\sqrt{1151919782703430}}{10}+442}{13431837.575}$$

Divide 442+\frac{\sqrt{1151919782703430}}{10} by 13431837.575 by multiplying 442+\frac{\sqrt{1151919782703430}}{10} by the reciprocal of 13431837.575.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

Now solve the equation x=\frac{442±\frac{\sqrt{1151919782703430}}{10}}{13431837.575} when ± is minus. Subtract \frac{\sqrt{1151919782703430}}{10} from 442.

$$x=\frac{-\frac{\sqrt{1151919782703430}}{10}+442}{13431837.575}$$

Divide 442-\frac{\sqrt{1151919782703430}}{10} by 13431837.575 by multiplying 442-\frac{\sqrt{1151919782703430}}{10} by the reciprocal of 13431837.575.

$$x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

The equation is now solved.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731} x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$

Steps for Completing the Square

Multiply both sides of the equation by 4745, the least common multiple of 365,65.

$$9663.1925\times 695x^{2}-13\times 34x=428802$$

Multiply 9663.1925 and 695 to get 6715918.7875.

$$6715918.7875x^{2}-13\times 34x=428802$$

Multiply -13 and 34 to get -442.

$$6715918.7875x^{2}-442x=428802$$

Divide both sides of the equation by 6715918.7875, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{6715918.7875x^{2}-442x}{6715918.7875}=\frac{428802}{6715918.7875}$$

Dividing by 6715918.7875 undoes the multiplication by 6715918.7875.

$$x^{2}+\left(-\frac{442}{6715918.7875}\right)x=\frac{428802}{6715918.7875}$$

Divide -442 by 6715918.7875 by multiplying -442 by the reciprocal of 6715918.7875.

$$x^{2}-\frac{2720}{41328731}x=\frac{428802}{6715918.7875}$$

Divide 428802 by 6715918.7875 by multiplying 428802 by the reciprocal of 6715918.7875.

$$x^{2}-\frac{2720}{41328731}x=\frac{469920}{7359911}$$

Divide -\frac{2720}{41328731}, the coefficient of the x term, by 2 to get -\frac{1360}{41328731}. Then add the square of -\frac{1360}{41328731} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{2720}{41328731}x+\left(-\frac{1360}{41328731}\right)^{2}=\frac{469920}{7359911}+\left(-\frac{1360}{41328731}\right)^{2}$$

Square -\frac{1360}{41328731} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}=\frac{469920}{7359911}+\frac{1849600}{1708064006070361}$$

Add \frac{469920}{7359911} to \frac{1849600}{1708064006070361} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}=\frac{1417747424865760}{22204832078914693}$$

Factor x^{2}-\frac{2720}{41328731}x+\frac{1849600}{1708064006070361}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1360}{41328731}\right)^{2}=\frac{1417747424865760}{22204832078914693}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1360}{41328731}\right)^{2}}=\sqrt{\frac{1417747424865760}{22204832078914693}}$$

Simplify.

$$x-\frac{1360}{41328731}=\frac{4\sqrt{1151919782703430}}{537273503} x-\frac{1360}{41328731}=-\frac{4\sqrt{1151919782703430}}{537273503}$$

Add \frac{1360}{41328731} to both sides of the equation.

$$x=\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731} x=-\frac{4\sqrt{1151919782703430}}{537273503}+\frac{1360}{41328731}$$