Question

Using the quadratic formula to solve 4x2-3x+9 = 2x+1 what are the values of x?

Answer 1

we know that

The formula to calculate the solutions of the quadratic equation of the form $ax^{2} +bx+c=0$  is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

in this problem we have

$4x^{2}-3x+9=2x+1$  

$4x^{2}-3x+9-2x-1=0$  

$4x^{2}-5x+8=0$  

$a=4\ b=-5\ c=8$

substitute in the formula

$x=\frac{-(-5)(+/-)\sqrt{(-5)^{2}-4(4)(8)}}{2*4}$

$x=\frac{5(+/-)\sqrt{25-128}}{8}$

$x=\frac{5(+/-)\sqrt{-103}}{8}$

remember that

$i=\sqrt{-1}$

$x=\frac{5(+/-)i\sqrt{103}}{8}$

therefore

the answer is

the solutions are

$x=\frac{5+i\sqrt{103}}{8}$

$x=\frac{5-i\sqrt{103}}{8}$

Answer 2

The value of $x$ which satisfies the given quadratic equation are  $\fbox{\begin\\\ \math x_{1}&=\dfrac{5+ i\sqrt{103}}{8} \ \ x_{2}&=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Further explanation:

The given equation is $4x^{2}-3x+9=2x+1$

From the given equation it is observed that the degree or the highest power of the variable is $2$.

This implies that the given equation is a quadratic equation.

A quadratic equation is an equation whose degree or the highest power of the variable is $2$.

To obtain the solutions of the given quadratic equation express the given equation in its simplest form i.e. collect all the variables on the left side of the equation.

$\begin{aligned}4x^{2}-3x+9&=2x+1\\4x^{2}-5x+8&=0\end{aligned}$

The above equation is a quadratic equation with its leading coefficient as $4$.

Since, the degree of a quadratic equation is $2$ so, the there are two roots of the given quadratic equation.

The solutions of a quadratic equation are the points where the curve of the function intersects the $x$-axis.

The solution of a quadratic equation of the form $ax^{2}+bx+c=0$ is calculated as follows:

$\fbox{\begin\\\ \math x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}\\\end{minispace}}$

The above formula is called the quadratic formula.

On comparing the quadratic equation $4x^{2}-5x+8=0$ with the general form of the quadratic equation it is observed that the value of $a$ is $4$, value of $b$ is $-5$ and the value of $c$ is $8$.

To obtain the solution of the given quadratic equation substitute the value of $a,b\ \text{and}\ c$ in the quadratic formula.

$\math x&=\dfrac{-(-5)\pm\sqrt{(-5)^{2}-4\times4\times8}}{2\times4}\\x&=\dfrac{5\pm\sqrt{25-128}}{8}\\x&=\dfrac{5\pm\sqrt{-103}}{8}\\x&=\dfrac{5\pm i\sqrt{103}}{8}$

In the above equation $i=\sqrt{-1}$

The first value of $x$ is as follows:

$\fbox{\begin\\\ \math x_{1}=\dfrac{5+ i\sqrt{103}}{8}\\\end{minispace}}$

The second value of $x$ is as follows:

$\fbox{\begin\\\ \math x_{2}=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Therefore, the two values of $x$ which satisfies the given quadratic function are as follows:

$\fbox{\begin\\\ \math x_{1}&=\dfrac{5+ i\sqrt{103}}{8} \ \ x_{2}&=\dfrac{5- i\sqrt{103}}{8}\\\end{minispace}}$

Learn more:

1. A problem on composite function https://brainly.com/question/2723982  

2. A problem to find radius and center of circle https://brainly.com/question/9510228  

3. A problem to determine intercepts of a line https://brainly.com/question/1332667  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Quadratic equation

Keywords: Quadratic, expression, equation, quadratic equation, solution, roots, highest power, degree, variables, leading coefficients, quadratic formula, x-axis, formula, general form.