Solve Using the Quadratic Formula 0.7x^2=1.4x+0.7

$0.7 x^{2} = 1.4 x + 0.7$

Step 1

Move all the expressions to the left side of the equation.

Subtract $1.4 x$ from both sides of the equation.

$0.7 x^{2} - 1.4 x = 0.7$

Subtract $0.7$ from both sides of the equation.

$0.7 x^{2} - 1.4 x - 0.7 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 0.7$ , $b = - 1.4$ , and $c = - 0.7$ into the quadratic formula and solve for $x$ .

$\frac{1.4 \pm \sqrt{{(- 1.4)}^{2} - 4 \cdot (0.7 \cdot - 0.7)}}{2 \cdot 0.7}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 1.4$ to the power of $2$ .

$x = \frac{1.4 \pm \sqrt{1.96 - 4 \cdot 0.7 \cdot - 0.7}}{2 \cdot 0.7}$

Multiply $- 4 \cdot 0.7 \cdot - 0.7$ .

Multiply $- 4$ by $0.7$ .

$x = \frac{1.4 \pm \sqrt{1.96 - 2.8 \cdot - 0.7}}{2 \cdot 0.7}$

Multiply $- 2.8$ by $- 0.7$ .

$x = \frac{1.4 \pm \sqrt{1.96 + 1.96}}{2 \cdot 0.7}$

Add $1.96$ and $1.96$ .

$x = \frac{1.4 \pm \sqrt{3.92}}{2 \cdot 0.7}$

Multiply $2$ by $0.7$ .

$x = \frac{1.4 \pm \sqrt{3.92}}{1.4}$

Simplify $\frac{1.4 \pm \sqrt{3.92}}{1.4}$ .

$x = \frac{7 \pm 5 \sqrt{3.92}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm 5 \sqrt{3.92}}{7}$

Decimal Form:

$x = 2.41421356 \dots, - 0.41421356 \dots$