This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The equation you provided, $2x+x-12=0$, simplifies to $3x-12=0$. This is a linear equation, not a quadratic equation. The quadratic formula is used for equations of the form $ax^2+bx+c=0$, where $a \neq 0$.
However, based on our previous conversation for question 21, it's possible you meant to ask about the quadratic equation $x^2+x-12=0$. I will solve this equation using the quadratic formula.
Solving $x^2+x-12=0$ using the quadratic formula:
Step 1: Identify the coefficients.
For a quadratic equation in the form $ax^2+bx+c=0$, we have:
$a = 1$
$b = 1$
$c = -12$
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 $c$:
$$x = \frac{-(1) \pm \sqrt{(1)^2 - 4(1)(-12)}}{2(1)}$$
Step 3: Simplify the expression under the square root.
$$x = \frac{-1 \pm \sqrt{1 - (-48)}}{2}$$
$$x = \frac{-1 \pm \sqrt{1 + 48}}{2}$$
$$x = \frac{-1 \pm \sqrt{49}}{2}$$
Step 4: Calculate the square root.
$$x = \frac{-1 \pm 7}{2}$$
Step 5: Find the two possible values for $x$.
For the positive root:
$$x_1 = \frac{-1 + 7}{2}$$
$$x_1 = \frac{6}{2}$$
$$x_1 = 3$$
For the negative root:
$$x_2 = \frac{-1 - 7}{2}$$
$$x_2 = \frac{-8}{2}$$
$$x_2 = -4$$
The possible values of $x$ are $3$ and $-4$.
The final answer is $\boxed{3, -4}$.
That's 2 down. 3 left today — send the next one.
Using quadratic equation
|Mathematics
ScanSolve AI Answer
The equation you provided, 2x+x−12=0, simplifies to 3x−12=0. This is a linear equation, not a quadratic equation. The quadratic formula is used for equations of the form ax2+bx+c=0, where a=0.
However, based on our previous conversation for question 21, it's possible you meant to ask about the quadratic equation x2+x−12=0. I will solve this equation using the quadratic formula.
Solving x2+x−12=0 using the quadratic formula:
Step 1: Identify the coefficients.
For a quadratic equation in the form ax2+bx+c=0, we have:
a=1b=1c=−12
Step 2: Apply the quadratic formula.
The quadratic formula is x=2a−b±b2−4ac.
Substitute the values of a, b, and c:
x=2(1)−(1)±(1)2−4(1)(−12)
Step 3: Simplify the expression under the square root.x=2−1±1−(−48)x=2−1±1+48x=2−1±49
Step 4: Calculate the square root.x=2−1±7
Step 5: Find the two possible values for x.
For the positive root:
x1=2−1+7x1=26x1=3
For the negative root:
x2=2−1−7x2=2−8x2=−4
The possible values of x are 3 and −4.
The final answer is 3,−4.
That's 2 down. 3 left today — send the next one.
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