solve a quadratic equation
x2+5x-14=0
Do you mean 2x+5x-14=0? If you do, this is how you would solve it:
2x+5x-14=0
2x+5x=14 (add 14 to both sides)
7x=14 (add 2x+5x together)
x=2 (divide both sides by 7)
x^2+5x-14 = (x-2)(x+7)
Oh, duh! It's been awhile since I had algebra.
To solve a quadratic equation, you can use the quadratic formula or complete the square method. Since the equation you provided is in the form of ax^2 + bx + c = 0, where a = 1, b = 5, and c = -14, let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Applying this to your equation, we have:
x = (-(5) ± √((5)^2 - 4(1)(-14))) / (2(1))
x = (-5 ± √(25 + 56)) / 2
x = (-5 ± √81) / 2
The square root of 81 is 9, so we have:
x = (-5 ± 9) / 2
Now let's find the values of x by considering both the positive and negative square root:
When evaluating with the positive square root:
x = (-5 + 9) / 2
x = 4 / 2
x = 2
When evaluating with the negative square root:
x = (-5 - 9) / 2
x = -14 / 2
x = -7
Therefore, the solutions to the quadratic equation x^2 + 5x - 14 = 0 are x = 2 and x = -7.