AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
How to Solve the Quadratic Equation $9x^2 + 888 = 444444$
Mathematics
Grade 8 of Junior High School
Question Content
Solve the equation: $9x^2 + 888 = 444444$
Correct Answer
$x = 220$ or $x = -220$
Detailed Solution Steps
1
Step 1: Isolate the quadratic term. Subtract 888 from both sides of the equation: $9x^2 = 444444 - 888$
2
Step 2: Calculate the right-hand side: $444444 - 888 = 443556$, so the equation becomes $9x^2 = 443556$
3
Step 3: Solve for $x^2$ by dividing both sides by 9: $x^2 = 443556 \\div 9 = 49284$
4
Step 4: Take the square root of both sides. Remember that square roots have positive and negative solutions: $x = \\pm\\sqrt{49284} = \\pm220$
Knowledge Points Involved
1
Isolation of variable terms in equations
This refers to rearranging an equation to get the term containing the unknown variable alone on one side, using inverse operations (addition/subtraction, multiplication/division) on both sides of the equation to maintain equality. It is a basic step for solving linear, quadratic and other types of equations.
2
Solving simple quadratic equations of the form $ax^2 = b$
For quadratic equations without a linear term (in the form $ax^2 = b$, where $a \\neq 0$ and $b/a \\geq 0$), the solution is obtained by first finding $x^2 = b/a$, then taking the square root of both sides, resulting in two solutions: $x = \\sqrt{b/a}$ and $x = -\\sqrt{b/a}$.
3
Properties of equality
The properties state that if the same number is added, subtracted, multiplied, or divided (by a non-zero number) to both sides of an equation, the equality still holds. These properties are the foundation for rearranging and solving all algebraic equations.
Loading solution...
