Which expression gives the solutions of –5 + 2x² = –6x?
To find the solutions of the equation -5 + 2x² = -6x, we need to set the equation equal to zero and solve for x.
First, let's move all terms to one side of the equation:
2x² + 6x - 5 = 0
Next, we can try factoring the quadratic equation, but this equation doesn't appear to be factorable. Therefore, we can solve it using the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / 2a
In our equation, a = 2, b = 6, and c = -5. Substituting these values into the quadratic formula, we get:
x = (-6 ± √(6² - 4(2)(-5))) / (2(2))
= (-6 ± √(36 + 40)) / 4
= (-6 ± √(76)) / 4
Simplifying further, we get:
x = (-6 ± √(76)) / 4
= (-6 ± √(4 * 19)) / 4
= (-6 ± 2√(19)) / 4
Now, we can simplify the expression further:
x = (-6 ± 2√(19)) / 4
= -3/2 ± (√19) / 2
Therefore, the expression that gives the solutions of the equation -5 + 2x² = -6x is:
x = -3/2 ± (√19) / 2
To find the solutions of the equation –5 + 2x² = –6x, we can rearrange the equation to form a quadratic equation of the form ax² + bx + c = 0.
Starting with –5 + 2x² = –6x, we can add 6x to both sides to move all the terms to one side:
2x² + 6x - 5 = 0
Now we have a quadratic equation in standard form. To solve the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Comparing the equation 2x² + 6x - 5 = 0 to ax² + bx + c = 0, we can see that a = 2, b = 6, and c = -5. Plugging these values into the quadratic formula, we get:
x = (-6 ± √(6² - 4(2)(-5))) / (2(2))
x = (-6 ± √(36 + 40)) / 4
x = (-6 ± √76) / 4
x = (-6 ± √(4 * 19)) / 4
x = (-6 ± 2√19) / 4
Simplifying the expression further, we can divide both the numerator and denominator by 2:
x = -3 ± √19 / 2
Therefore, the expression that gives the solutions of –5 + 2x² = –6x is x = -3 ± √19 / 2.
-5 + 2x^2 = -6x
2x^2 + 6x - 5 = 0
x = (-6 ± √(36 - 4(2)(-5))/4
= (-6 ± √76)/4
= (-6 ± 2√19)/4
= (-3 ± √19)/2