Solve 3.8m^2=1.8m+10/2*1.3m

$$3.8 m ^ { 2 } = \frac { 1.8 m + 10 } { 2 } \cdot 1.3 m$$

Solve for m

$$m = \frac{650}{263} = 2\frac{124}{263} \approx 2.47148289$$

$$m=0$$

Steps Using Factoring

Multiply both sides of the equation by 2.

$$7.6m^{2}=\left(1.8m+10\right)\times 1.3m$$

Use the distributive property to multiply 1.8m+10 by 1.3.

$$7.6m^{2}=\left(2.34m+13\right)m$$

Use the distributive property to multiply 2.34m+13 by m.

$$7.6m^{2}=2.34m^{2}+13m$$

Subtract 2.34m^{2} from both sides.

$$7.6m^{2}-2.34m^{2}=13m$$

Combine 7.6m^{2} and -2.34m^{2} to get 5.26m^{2}.

$$5.26m^{2}=13m$$

Subtract 13m from both sides.

$$5.26m^{2}-13m=0$$

Factor out m.

$$m\left(5.26m-13\right)=0$$

To find equation solutions, solve m=0 and \frac{263m}{50}-13=0.

$$m=0 m=\frac{650}{263}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$7.6m^{2}=\left(1.8m+10\right)\times 1.3m$$

Use the distributive property to multiply 1.8m+10 by 1.3.

$$7.6m^{2}=\left(2.34m+13\right)m$$

Use the distributive property to multiply 2.34m+13 by m.

$$7.6m^{2}=2.34m^{2}+13m$$

Subtract 2.34m^{2} from both sides.

$$7.6m^{2}-2.34m^{2}=13m$$

Combine 7.6m^{2} and -2.34m^{2} to get 5.26m^{2}.

$$5.26m^{2}=13m$$

Subtract 13m from both sides.

$$5.26m^{2}-13m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5.26 for a, -13 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}}}{2\times 5.26}$$

Take the square root of \left(-13\right)^{2}.

$$m=\frac{-\left(-13\right)±13}{2\times 5.26}$$

The opposite of -13 is 13.

$$m=\frac{13±13}{2\times 5.26}$$

Multiply 2 times 5.26.

$$m=\frac{13±13}{10.52}$$

Now solve the equation m=\frac{13±13}{10.52} when ± is plus. Add 13 to 13.

$$m=\frac{26}{10.52}$$

Divide 26 by 10.52 by multiplying 26 by the reciprocal of 10.52.

$$m=\frac{650}{263}$$

Now solve the equation m=\frac{13±13}{10.52} when ± is minus. Subtract 13 from 13.

$$m=\frac{0}{10.52}$$

Divide 0 by 10.52 by multiplying 0 by the reciprocal of 10.52.

$$m=0$$

The equation is now solved.

$$m=\frac{650}{263} m=0$$

Steps for Completing the Square

Multiply both sides of the equation by 2.

$$7.6m^{2}=\left(1.8m+10\right)\times 1.3m$$

Use the distributive property to multiply 1.8m+10 by 1.3.

$$7.6m^{2}=\left(2.34m+13\right)m$$

Use the distributive property to multiply 2.34m+13 by m.

$$7.6m^{2}=2.34m^{2}+13m$$

Subtract 2.34m^{2} from both sides.

$$7.6m^{2}-2.34m^{2}=13m$$

Combine 7.6m^{2} and -2.34m^{2} to get 5.26m^{2}.

$$5.26m^{2}=13m$$

Subtract 13m from both sides.

$$5.26m^{2}-13m=0$$

Divide both sides of the equation by 5.26, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{5.26m^{2}-13m}{5.26}=\frac{0}{5.26}$$

Dividing by 5.26 undoes the multiplication by 5.26.

$$m^{2}+\left(-\frac{13}{5.26}\right)m=\frac{0}{5.26}$$

Divide -13 by 5.26 by multiplying -13 by the reciprocal of 5.26.

$$m^{2}-\frac{650}{263}m=\frac{0}{5.26}$$

Divide 0 by 5.26 by multiplying 0 by the reciprocal of 5.26.

$$m^{2}-\frac{650}{263}m=0$$

Divide -\frac{650}{263}, the coefficient of the x term, by 2 to get -\frac{325}{263}. Then add the square of -\frac{325}{263} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{650}{263}m+\left(-\frac{325}{263}\right)^{2}=\left(-\frac{325}{263}\right)^{2}$$

Square -\frac{325}{263} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{650}{263}m+\frac{105625}{69169}=\frac{105625}{69169}$$

Factor m^{2}-\frac{650}{263}m+\frac{105625}{69169}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{325}{263}\right)^{2}=\frac{105625}{69169}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{325}{263}\right)^{2}}=\sqrt{\frac{105625}{69169}}$$

Simplify.

$$m-\frac{325}{263}=\frac{325}{263} m-\frac{325}{263}=-\frac{325}{263}$$

Add \frac{325}{263} to both sides of the equation.

$$m=\frac{650}{263} m=0$$