Q. The equation −4x2+7=12x is rewritten in the form of −4(x−p)2+q=0. What is the value of q ?(A) −2(B) 419(C) 437(D) 16
Rewrite in Standard Form: Rewrite the given equation in standard quadratic form.The given equation is −4x2+7=12x. To rewrite it in standard form, we need to move all terms to one side of the equation.−4x2−12x+7=0
Complete the Square:Complete the square to rewrite the equation in the form of −4(x−p)2+q=0. First, we factor out the coefficient of x2, which is −4, from the x terms. −4(x2+3x)+7=0 Next, we find the value that completes the square for the expression x2+3x. This value is (b/2)2, where b is the coefficient of x, which is 3 in this case. x20 We add and subtract x21 inside the parentheses to complete the square, remembering to multiply the subtracted term by −4 to keep the equation balanced. x23x24
Simplify Further: Simplify the equation further.Now we have −4(x+23)2+9+7=0.Combine the constant terms outside the parentheses.−4(x+23)2+16=0
Identify Value of q: Identify the value of q in the equation −4(x−p)2+q=0.From the simplified equation, we can see that q is the constant term, which is 16.
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