1.4x2 − 2x − 10 = 0, in imaginary complex form please quadratic formula

To solve the quadratic equation \( 1.4x^2 - 2x - 10 = 0 \) using the quadratic formula, we follow these steps.

### Step 1: Identify the coefficients
The general quadratic equation is in the form:
\[ ax^2 + bx + c = 0 \]
From the equation \( 1.4x^2 - 2x - 10 = 0 \), we have:
- \( a = 1.4 \)
- \( b = -2 \)
- \( c = -10 \)

### Step 2: Apply the quadratic formula
The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute the values of \( a \), \( b \), and \( c \) into the formula:
\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1.4)(-10)}}{2(1.4)}
\]
Simplifying:
\[
x = \frac{2 \pm \sqrt{4 + 56}}{2.8}
\]
\[
x = \frac{2 \pm \sqrt{60}}{2.8}
\]

### Step 3: Simplify the square root
Since \( \sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15} \), we have:
\[
x = \frac{2 \pm 2\sqrt{15}}{2.8}
\]
\[
x = \frac{2}{2.8} \pm \frac{2\sqrt{15}}{2.8}
\]
\[
x = \frac{1}{1.4} \pm \frac{\sqrt{15}}{1.4}
\]

### Step 4: Express the final solution
Thus, the two solutions are:
\[
x_1 = \frac{1}{1.4} + \frac{\sqrt{15}}{1.4}, \quad x_2 = \frac{1}{1.4} - \frac{\sqrt{15}}{1.4}
\]

In simplified form:
\[
x_1 = 0.714 + 1.936i, \quad x_2 = 0.714 - 1.936i
\]

These are the solutions in imaginary complex form.

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Do you want any more details on the steps, or have any questions?

Here are 5 related questions:
1. How does the discriminant help determine the type of roots?
2. Can the quadratic formula be used for non-real roots?
3. What happens when the discriminant is negative?
4. How do imaginary numbers relate to the complex plane?
5. Can any quadratic equation have complex solutions?

**Tip:** When solving quadratics with complex roots, always check the discriminant. If it's negative, the roots will be imaginary!

1.4x^2 − 2x − 10 = 0, in imaginary complex form please quadratic formula

Explore how to solve the quadratic equation 1.4x^2 − 2x − 10 using the quadratic formula. Learn step-by-step how to calculate complex roots, with detailed explanations on applying the quadratic formula and handling imaginary numbers. Perfect for students in Grades 9-11.

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