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Help with Quadratics?
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Help with Quadratics?
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| 28/12 2013 22:21
Reorder: 50 - 2(x + 1)^2 = -2(x + 1)^2 + 50 Divide both terms by -2: (x + 1)^2 - 25 This is a difference of two squares of the form a^2 - b^2 = (a + b)(a - b): (x + 1) + 5)(x + 1 - 5) Simplify: (x + 6)(x - 4) Check this: (x + 6)(x + 4) = x^2 + 6x - 4x - 24 = x^2 + 2x - 24 (x + 1)^2 - 25 = (x + 1)(x + 1) - 25 = (x^2 + 2x + 1) - 25 = x^2 + 2x - 24 So this is your final solution: (x + 6)(x - 4)
| 28/12 2013 22:44
50 - 2( x + 1 )² 1) According to the rules for Order of Operations, you do the exponent first. So you have to square ( x + 1 ) When you have finished multiplying ( x + 1 )( x + 1 ), this is what you get: 50 - 2 ( x² + 2x + 1 ) 2) Next you clear the parentheses by distributing the - 2 After you distribute, you get this: 50 - 2x² - 4x - 2 3) Combine like terms, giving you this: - 2x² - 4x - 52 4) Factor After you factor out the greatest common factor, which is - 2, you get this: - 2 ( x² + 2x + 26 ) <-- answer
| 28/12 2013 23:05
Factor out 2, giving 2(25 - (x+1)²) Note that 25 = 5². The content of the outermost parentheses is an example of the difference between two squares: 25 - (x+1)² = 5² - (x+1)² = (5 - (x+1))(5 + (x+1)) = (4 - x)(6 + x) So the whole expression becomes 2(4 - x)(6 + x) You might want both x's to be positive within each set of parentheses. To achieve this, factor out a "minus" sign. SOLUTION: 50 - 2(x+1)² = -2(x - 4)(6 + x) —————————————————— [Note that you can't randomly omit the -2 from your answer!] ——————————————————
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