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Solve for x. {:[4x^(2)-48 x+144=0],[x=◻]:}

Solve for x x .\newline4x2−48x+144=0x=□ \begin{array}{l} 4 x^{2}-48 x+144=0 \\ x=\square \end{array}

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Q. Solve for x x .\newline4x2−48x+144=0x=□ \begin{array}{l} 4 x^{2}-48 x+144=0 \\ x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is 4x2−48x+144=04x^2 - 48x + 144 = 0.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to give the product of the first coefficient 44 and the constant term 144144, which is 4×144=5764 \times 144 = 576, and add up to the middle coefficient −48-48.\newlineThe numbers that satisfy these conditions are −24-24 and −24-24, since (−24)×(−24)=576(-24) \times (-24) = 576 and (−24)+(−24)=−48(-24) + (-24) = -48.
  3. Write the factored form: Write the factored form of the equation.\newlineThe factored form of the equation is (4x−24)(x−6)=0(4x - 24)(x - 6) = 0.
  4. Set each factor equal to zero and solve for x: Set each factor equal to zero and solve for x.\newlineFirst factor: 4x−24=04x - 24 = 0\newlineAdd 2424 to both sides: 4x=244x = 24\newlineDivide by 44: x=6x = 6\newlineSecond factor: x−6=0x - 6 = 0\newlineAdd 66 to both sides: x=6x = 6\newlineWe find that both factors give the same solution for xx.

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