Solve 4.24x^2-0.848x+0.0424=0

$$4.24 { x }^{ 2 } -0.848x+0.0424 = 0$$

Solve for x

$$x=0.1$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$4.24x^{2}-0.848x+0.0424=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4.24 for a, -0.848 for b, and 0.0424 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-0.848\right)±\sqrt{\left(-0.848\right)^{2}-4\times 4.24\times 0.0424}}{2\times 4.24}$$

Square -0.848 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\left(-0.848\right)±\sqrt{0.719104-4\times 4.24\times 0.0424}}{2\times 4.24}$$

Multiply -4 times 4.24.

$$x=\frac{-\left(-0.848\right)±\sqrt{0.719104-16.96\times 0.0424}}{2\times 4.24}$$

Multiply -16.96 times 0.0424 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.848\right)±\sqrt{\frac{11236-11236}{15625}}}{2\times 4.24}$$

Add 0.719104 to -0.719104 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\left(-0.848\right)±\sqrt{0}}{2\times 4.24}$$

Take the square root of 0.

$$x=-\frac{-0.848}{2\times 4.24}$$

The opposite of -0.848 is 0.848.

$$x=\frac{0.848}{2\times 4.24}$$

Multiply 2 times 4.24.

$$x=\frac{0.848}{8.48}$$

Divide 0.848 by 8.48 by multiplying 0.848 by the reciprocal of 8.48.

$$x=0.1$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$4.24x^{2}-0.848x+0.0424=0$$

Subtract 0.0424 from both sides of the equation.

$$4.24x^{2}-0.848x+0.0424-0.0424=-0.0424$$

Subtracting 0.0424 from itself leaves 0.

$$4.24x^{2}-0.848x=-0.0424$$

Divide both sides of the equation by 4.24, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{4.24x^{2}-0.848x}{4.24}=-\frac{0.0424}{4.24}$$

Dividing by 4.24 undoes the multiplication by 4.24.

$$x^{2}+\left(-\frac{0.848}{4.24}\right)x=-\frac{0.0424}{4.24}$$

Divide -0.848 by 4.24 by multiplying -0.848 by the reciprocal of 4.24.

$$x^{2}-0.2x=-\frac{0.0424}{4.24}$$

Divide -0.0424 by 4.24 by multiplying -0.0424 by the reciprocal of 4.24.

$$x^{2}-0.2x=-0.01$$

Divide -0.2, the coefficient of the x term, by 2 to get -0.1. Then add the square of -0.1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-0.2x+\left(-0.1\right)^{2}=-0.01+\left(-0.1\right)^{2}$$

Square -0.1 by squaring both the numerator and the denominator of the fraction.

$$x^{2}-0.2x+0.01=\frac{-1+1}{100}$$

Add -0.01 to 0.01 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-0.2x+0.01=0$$

Factor x^{2}-0.2x+0.01. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-0.1\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-0.1\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-0.1=0 x-0.1=0$$

Add 0.1 to both sides of the equation.

$$x=0.1 x=0.1$$

The equation is now solved. Solutions are the same.

$$x=0.1$$