Solve the equation 3x^2+7x+14=−7x to the nearest tenth
Please help this is overdue and its for Deltamath.com
Please
3x^2+ 14 x+14= 0
-3.22 , -1.45
To solve the equation 3x^2 + 7x + 14 = -7x to the nearest tenth, follow these steps:
Step 1: Combine like terms.
3x^2 + 7x + 14 + 7x = 0
Step 2: Simplify the equation.
3x^2 + 14x + 14 = 0
Step 3: Use the quadratic formula to solve for x.
The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 3, b = 14, and c = 14.
x = (-14 ± √(14^2 - 4(3)(14))) / (2(3))
x = (-14 ± √(196 - 168)) / 6
x = (-14 ± √(28)) / 6
x = (-14 ± √(4 * 7)) / 6
x = (-14 ± 2√7) / 6
Step 4: Simplify the solutions.
To find the solutions to the nearest tenth, we can evaluate both of the possibilities for x:
x1 = (-14 + 2√7) / 6
x2 = (-14 - 2√7) / 6
Evaluating x1:
x1 = (-14 + 2√7) / 6 ≈ -2.23
Evaluating x2:
x2 = (-14 - 2√7) / 6 ≈ -1.44
Therefore, the solutions to the equation 3x^2 + 7x + 14 = -7x to the nearest tenth are approximately -2.2 and -1.4.