21 + + = x^2 7x 5 0 One solution to the given equation can be written as -7 k = x (+)/2, where k is a constant. What is the value of k?
","rationale_html":"29 The correct answer is . The solutions to a quadratic equation in the form 2+ + =0 ax bx c , where a, b, and c are constants, can be calculated using the - + 2-4 = b b ac quadratic formula, which gives two solutions: x 2 and = - b - b 2-4 ac 2+ a + =0 = x 2 . The given equation is in the form ax bx c , where a 1, a = = b 7, and c 5. It follows that one solution to the given quadratic equation is -7+ 72-4 1 5 -7+ 49-20 -7+ 29 x = 2 1 ] g] g , or x = 2 , which is equivalent to x = 2 . It’s ] g -7+ = k given that one solution to the given equation can be written as x 2 , where 29 k is a constant. It follows that the value of k is .
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