What is the positive solution to x² + 5x - 36 = 0?
Understand the Problem
The question is asking for the positive solution to the quadratic equation x² + 5x - 36 = 0. To solve it, we can use the quadratic formula or factor the equation.
Answer
The positive solution is $x = 4$.
Answer for screen readers
The positive solution to the equation $x^2 + 5x - 36 = 0$ is $x = 4$.
Steps to Solve
- Identify the coefficients For the quadratic equation $x^2 + 5x - 36 = 0$, the coefficients are:
- $a = 1$ (coefficient of $x^2$)
- $b = 5$ (coefficient of $x$)
- $c = -36$ (constant term)
- Use the quadratic formula The quadratic formula is given by:
$$ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} $$
Substituting the coefficients into the formula:
$$ x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot (-36)}}}}{2 \cdot 1} $$
- Calculate the discriminant First, calculate $b^2 - 4ac$:
$$ 5^2 - 4 \cdot 1 \cdot (-36) = 25 + 144 = 169 $$
- Calculate the square root Now find the square root of the discriminant:
$$ \sqrt{169} = 13 $$
- Find the possible values of x Substituting back into the quadratic formula:
$$ x = \frac{{-5 \pm 13}}{2} $$
We have two solutions:
- For $x = \frac{{-5 + 13}}{2}$:
$$ x = \frac{8}{2} = 4 $$
- For $x = \frac{{-5 - 13}}{2}$:
$$ x = \frac{-18}{2} = -9 $$
- Identify the positive solution The positive solution is $x = 4$.
The positive solution to the equation $x^2 + 5x - 36 = 0$ is $x = 4$.
More Information
The quadratic formula can always be used to find solutions to any quadratic equation and is derived from completing the square method. The positive solution indicates that there can be more than one solution, typical in quadratics.
Tips
- Forgetting to simplify the square root can lead to incorrect solutions.
- Mixing up the signs while applying the quadratic formula can also yield wrong answers.
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