What expression gives the solutions of -5+2x^2=-6x?
rearranging ... 2 x^2 + 6 x - 5 = 0
use the quadratic formula to find the solutions
Okay, thank you.
To find the solutions of the equation -5 + 2x^2 = -6x, we can follow these steps:
Step 1: Start by rewriting the equation in standard form, which means setting it equal to zero.
2x^2 + 6x - 5 = 0
Step 2: Next, check if the equation can be factored. If it can, factor the equation and set each factor equal to zero.
Since the equation doesn't have simple integer factors, we will use the quadratic formula.
Step 3: The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, we have a = 2, b = 6, and c = -5. Substituting these values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4(2)(-5)))/(2(2))
x = (-6 ± √(36 + 40))/(4)
x = (-6 ± √(76))/(4)
Step 4: Simplify the expression under the square root.
x = (-6 ± √(76))/(4)
x = (-6 ± √(4 * 19))/(4)
x = (-6 ± 2√(19))/(4)
Step 5: Simplify the expression by factoring out a 2 from the numerator and denominator.
x = (-3 ± √(19))/(2)
So, the expression that gives the solutions of -5 + 2x^2 = -6x is x = (-3 ± √(19))/(2).
To find the values of x that satisfy the equation -5 + 2x^2 = -6x, we can rearrange the equation to form a quadratic equation. The steps are as follows:
Step 1: Move all the terms to one side of the equation to set it equal to zero.
-5 + 2x^2 + 6x = 0
Step 2: Combine like terms.
2x^2 + 6x - 5 = 0
Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 6, and c = -5.
Step 3: To solve this quadratic equation, we can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c from our equation, we get:
x = (-(6) ± √((6)^2 - 4(2)(-5))) / (2(2))
Simplifying further:
x = (-6 ± √(36 + 40)) / 4
x = (-6 ± √76) / 4
Step 4: We can simplify the square root of 76.
√76 = √(4*19) = 2√19
Substituting this back into our equation:
x = (-6 ± 2√19) / 4
Step 5: Finally, we can simplify the expression.
x = -3 ± √19/2
Therefore, the expression that gives the solutions for -5 + 2x^2 = -6x is x = -3 ± √19/2.