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Find each product and write the result in standard form. (7 - 5i)(- 2 - 3i)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 13
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 3) = x - 3
Guida verificata passo dopo passo1
Start by isolating the radical expression, which is already isolated as \( \sqrt{\!x + 3} = x - 3 \).
Square both sides of the equation to eliminate the square root. This gives \( (\sqrt{\!x + 3})^2 = (x - 3)^2 \), which simplifies to \( x + 3 = (x - 3)^2 \).
Expand the right side using the formula \( (a - b)^2 = a^2 - 2ab + b^2 \). So, \( (x - 3)^2 = x^2 - 6x + 9 \). Substitute this back to get \( x + 3 = x^2 - 6x + 9 \).
Rearrange the equation to set it equal to zero: \( 0 = x^2 - 6x + 9 - x - 3 \), which simplifies to \( 0 = x^2 - 7x + 6 \).
Solve the quadratic equation \( x^2 - 7x + 6 = 0 \) by factoring, completing the square, or using the quadratic formula. After finding the solutions, check each one in the original equation to ensure they do not produce extraneous solutions.
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Radical Equations
Radical equations involve variables inside a root, often a square root. To solve them, isolate the radical expression and then eliminate the root by raising both sides to the appropriate power, typically squaring for square roots.
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Expanding Radicals
Extraneous Solutions
When solving radical equations by squaring both sides, new solutions may appear that do not satisfy the original equation. These are called extraneous solutions and must be checked by substituting back into the original equation.
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06:00Categorizing Linear Equations
Domain Restrictions
The expression inside a square root must be non-negative for real solutions. This restriction limits the domain of the variable and must be considered before solving to avoid invalid solutions.
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3:51Domain Restrictions of Composed Functions
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