I have a few match problems that I can't figure out.
1.solve: 3x+5=x√7 (that's a radical sign)
2.factor: (2k+3)2-(2x+3)(y-2)-20(y-2)2 (the "2" after (2k+3) ans (y-2) is suppose to be a square sign.
thanks if you can help, or even if you can't
i ment "Math" lol
No problem, I'm here to help you with your math problems!
1. Solve: 3x + 5 = x√7
To solve this equation, we need to isolate the variable x. Let's break it down step by step:
Step 1: Get rid of the radical symbol (√) by squaring both sides of the equation.
(3x + 5)² = (x√7)²
Step 2: Simplify the equation by expanding the squared expressions.
9x² + 30x + 25 = x² * 7
Step 3: Combine like terms and move all terms to one side of the equation.
9x² + 30x + 25 - 7x² = 0
Step 4: Arrange the terms to form a quadratic equation.
2x² + 30x + 25 = 0
Step 5: Solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, factoring is a good approach.
Factor the quadratic equation: (2x + 5)(x + 5) = 0
Now, set each factor equal to zero and solve for x:
2x + 5 = 0 or x + 5 = 0
Solving for x gives us two possible solutions:
2x = -5 --> x = -5/2
x = -5
So the equation 3x + 5 = x√7 has two solutions: x = -5/2 or x = -5.
2. Factor: (2k + 3)² - (2x + 3)(y - 2) - 20(y - 2)²
To factor this expression, notice that we have a common factor: (y - 2). Let's take it out as a common factor:
(y - 2)[(2k + 3)² - (2x + 3) - 20(y - 2)]
Now, let's simplify the expression inside the square brackets:
(2k + 3)² - (2x + 3) - 20(y - 2)
Expand the square: (2k + 3)(2k + 3) = 4k² + 12k + 9
Now substitute the simplified expression back into the factored form:
(y - 2)[4k² + 12k + 9 - (2x + 3) - 20(y - 2)]
Simplify further by distributing the negative sign and simplifying like terms:
(y - 2)[4k² + 12k + 9 - 2x - 3 - 20y + 40]
Now combine like terms:
(y - 2)[4k² + 12k - 2x + 46 - 20y]
Finally, the fully factored form of the expression is:
(y - 2)(4k² + 12k - 2x + 46 - 20y)
So the factored form of (2k + 3)² - (2x + 3)(y - 2) - 20(y - 2)² is (y - 2)(4k² + 12k - 2x + 46 - 20y).
I hope these explanations were helpful! If you have any more questions, feel free to ask.