Tlark10 said:Homework Statement
I can't determine where the 40x comes from.
From: 4x + 5 = 8√(1 - x)
To: 16x^2 +40x + 25 = 64 - 64x^2
Homework Equations
√1-x^2 = √1-x *√x+1
The Attempt at a Solution
4x + 5 = 8√(1-x)
4x^2 + 5^2 = (8 - 8x)*(8x + 8)
16x^2 +25 = 64 - 64x^2
I am not sure what you mean?Math_QED said:What is (a+b)^2 equal to?
(a+b)^2 = a^2 + b^2Math_QED said:What is (a+b)^2 equal to?
Tlark10 said:(a+b)^2 = a^2 + b^2
Ahhhh I see, thank you!Math_QED said:this is a frequently made mistake.
Well (a+b)^2 = (a+b)(a+b) = ...
Use distributivity
What you wrote as a relevant equation doesn't apply here. ##[8\sqrt{1 - x}]^2 \ne (8 - 8x)(8x + 8)##Tlark10 said:Homework Statement
I can't determine where the 40x comes from.
From: 4x + 5 = 8√(1 - x)
To: 16x^2 +40x + 25 = 64 - 64x^2
Homework Equations
√1-x^2 = √1-x *√x+1
The Attempt at a Solution
4x + 5 = 8√(1-x)
4x^2 + 5^2 = (8 - 8x)*(8x + 8)
Tlark10 said:16x^2 +25 = 64 - 64x^2
chwala said:alternatively ##4x+5=8√(1-x)##, can be expressed as, ##(4x+5)^2=64(1-x)##
chwala said:ok elaborate please.
The basic idea is that if you square both sides of an equation, the new equation might have solutions that don't satisfy the original equation. Here's a very simple example:chwala said:ok elaborate please.
To solve a quadratic equation, you can use the quadratic formula or factoring method. The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. Factoring involves finding two numbers that multiply to c and add to b, which can then be used to rewrite the equation in the form (x + m)(x + n) = 0, where m and n are the two numbers.
The purpose of solving a quadratic equation is to find the values of x that make the equation true. In other words, it helps us find the solutions or roots of the equation, which can be useful in many real-world applications such as finding the maximum or minimum value of a function.
No, a quadratic equation can have at most two solutions. This is because a quadratic equation is a polynomial of degree 2, which means it can have a maximum of 2 distinct roots. However, some equations may have repeated solutions, resulting in only one distinct solution.
If the quadratic equation has complex solutions, it means that the solutions involve imaginary numbers. This can happen when the discriminant b² - 4ac is negative. In this case, the solutions will be in the form of x = (-b ± √(b² - 4ac)i) / 2a, where i is the imaginary unit.
Yes, there are many resources available online that can help you solve a quadratic equation step-by-step. You can also seek help from a math tutor or teacher who can guide you through the process and explain any concepts that you may not understand.