Textbook Question
Which equation has two real, distinct solutions? Do not actually solve.
A. (3x-4)² = -9 B. (4-7x)² = 0 C. (5x-9)(5x-9) = 0 D. (7x+4)² = 11
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1. Equations & Inequalities
The Square Root Property
1:43 minutesProblem 4
Textbook Question
Match the equation in Column I with its solution(s) in Column II. x2 - 5 = 0
Verified step by step guidance1
Start with the given equation: \(x^2 - 5 = 0\).
Isolate the squared term by adding 5 to both sides: \(x^2 = 5\).
To solve for \(x\), take the square root of both sides: \(x = \pm \sqrt{5}\).
Remember that taking the square root introduces both positive and negative solutions, so the solutions are \(x = \sqrt{5}\) and \(x = -\sqrt{5}\).
Match these solutions with the corresponding option in Column II that lists \(x = \pm \sqrt{5}\).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solving Quadratic Equations
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solving it involves finding values of x that satisfy the equation, often by factoring, completing the square, or using the quadratic formula.
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Isolating the Variable
Isolating the variable means manipulating the equation to get the variable alone on one side. For example, in x² - 5 = 0, adding 5 to both sides isolates x², making it easier to solve for x by taking square roots.
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05:28Equations with Two Variables
Square Root Property
The square root property states that if x² = k, then x = ±√k. This means when solving equations like x² = 5, the solutions are both the positive and negative square roots of 5, reflecting two possible values for x.
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