To solve the equation \( 4x^2 + 9x - 11 = 2x^2 + 10x \), we first rearrange all terms to one side of the equation.
Starting with the original equation:
\[ 4x^2 + 9x - 11 = 2x^2 + 10x \]
Subtract \( 2x^2 \) and \( 10x \) from both sides:
\[ 4x^2 - 2x^2 + 9x - 10x - 11 = 0 \]
This simplifies to:
\[ 2x^2 - x - 11 = 0 \]
Now, we can use the quadratic formula to solve for \( x \). The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation \( 2x^2 - x - 11 = 0\), we can identify \( a = 2 \), \( b = -1 \), and \( c = -11 \).
First, we calculate the discriminant \( b^2 - 4ac \):
\[ b^2 - 4ac = (-1)^2 - 4(2)(-11) \] \[ = 1 + 88 \] \[ = 89 \]
Now we can apply the quadratic formula:
\[ x = \frac{-(-1) \pm \sqrt{89}}{2(2)} \] \[ = \frac{1 \pm \sqrt{89}}{4} \]
Next, we calculate \( \sqrt{89} \), which is approximately \( 9.434 \).
So, we have:
\[ x = \frac{1 + 9.434}{4} \quad \text{and} \quad x = \frac{1 - 9.434}{4} \]
Calculating the first solution:
\[ x \approx \frac{10.434}{4} \approx 2.6085 \]
Calculating the second solution:
\[ x \approx \frac{-8.434}{4} \approx -2.1085 \]
Rounding both answers to the nearest tenth, we find:
- \( x \approx 2.6 \)
- \( x \approx -2.1 \)
Therefore, the solutions to the equation are:
\[ x \approx 2.6 \quad \text{and} \quad x \approx -2.1 \]