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Solve for x. Enter the solutions from least to greatest. {:[4x^(2)+40 x+84=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline4x2+40x+84=0 lesser x=□ greater x=□ \begin{array}{l} 4 x^{2}+40 x+84=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Q. Solve for x x . Enter the solutions from least to greatest.\newline4x2+40x+84=0 lesser x=□ greater x=□ \begin{array}{l} 4 x^{2}+40 x+84=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineGiven equation: 4x2+40x+84=04x^2 + 40x + 84 = 0
  2. Factor out the greatest common factor: Factor out the greatest common factor (GCF) from the quadratic equation.\newlineThe GCF of 4x24x^2, 40x40x, and 8484 is 44.\newlineDivide each term by 44 to simplify the equation: (4x2)/4+(40x)/4+84/4=0/4(4x^2)/4 + (40x)/4 + 84/4 = 0/4\newlineThis simplifies to: x2+10x+21=0x^2 + 10x + 21 = 0
  3. Find two numbers that satisfy the conditions: Find two numbers that multiply to 2121 and add up to 1010.\newlineThe numbers 33 and 77 satisfy these conditions because 3×7=213 \times 7 = 21 and 3+7=103 + 7 = 10.
  4. Write the factored form of the quadratic equation: Write the factored form of the quadratic equation using the numbers found in the previous step. \newlinex2+10x+21=(x+3)(x+7)=0x^2 + 10x + 21 = (x + 3)(x + 7) = 0
  5. Solve for x using each factor: Set each factor equal to zero and solve for x.\newlineFirst factor: x+3=0x + 3 = 0\newlineSubtract 33 from both sides: x=−3x = -3\newlineSecond factor: x+7=0x + 7 = 0\newlineSubtract 77 from both sides: x=−7x = -7
  6. List the solutions in ascending order: List the solutions in ascending order.\newlineThe solutions are x=−7x = -7 and x=−3x = -3, with −7-7 being the lesser value and −3-3 being the greater value.

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