1. x^2 = 16
2. 2x(x+3) = 0
3. y^2 + 8y = 0
4. x^2 + 3x = 28
5. 2x^2 + 9x - 5 = 0
Margie, when you have answered these the best you can, please re-post and someone here will be happy to give you suggestions and let you know where you need to make corrections. Please keep in mind that we don't do students' homework for them.
hint:
these are all quadratic equations and all of them factor.
So expand if necessary, bring all the terms to the left side and set them equal to zero.
Factor them and from the factors determine the solutions.
I am sure they have shown you how to do that.
1. To find the value of x that satisfies the equation x^2 = 16, you can take the square root of both sides of the equation. Since the square root of 16 is 4 or -4, we have two possible values for x: x = 4 or x = -4.
2. To solve the equation 2x(x+3) = 0, we can use the zero-product property. This property states that if a product of two factors is equal to zero, then at least one of the factors must be zero. So, we set each factor equal to zero and solve for x:
Setting 2x = 0, we find x = 0.
Setting (x+3) = 0, we find x = -3.
Therefore, the solutions to the equation are x = 0 and x = -3.
3. The equation y^2 + 8y = 0 can be factored by taking out the common factor y: y(y + 8) = 0. Now, we have two factors, and according to the zero-product property, at least one of them must be zero. So, setting each factor equal to zero, we find two solutions: y = 0 and y = -8.
4. To solve the equation x^2 + 3x = 28, we can rearrange it to the form x^2 + 3x - 28 = 0. This is a quadratic equation, and we can solve it by factoring or using the quadratic formula. Factoring the left side, we have (x + 7)(x - 4) = 0. Setting each factor equal to zero, we find x = -7 and x = 4 as the solutions.
5. The equation 2x^2 + 9x - 5 = 0 is also a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Factoring this equation doesn't yield two integers that multiply to -10 and add up to 9, so we can resort to the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / (2a). By applying this formula to the given equation, we get two solutions: x ≈ -2.5 and x ≈ 0.5.