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Find one value of x that is a solution to the equation: {:[(2x+3)^(2)-6x-9=0],[x=◻]:}

Find one value of x x that is a solution to the equation:\newline(2x+3)2−6x−9=0 (2 x+3)^{2}-6 x-9=0 \newlinex= x=

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Solve a quadratic equation by factoringright chevron icon

Full solution

Q. Find one value of x x that is a solution to the equation:\newline(2x+3)2−6x−9=0 (2 x+3)^{2}-6 x-9=0 \newlinex= x=
  1. Write Equation: Write down the given equation.\newline(2x+3)2−6x−9=0(2x+3)^2 - 6x - 9 = 0
  2. Expand Squared Term: Expand the squared term (2x+3)2(2x+3)^2.
    (2x+3)(2x+3)−6x−9=0(2x+3)(2x+3) - 6x - 9 = 0
    4x2+6x+6x+9−6x−9=04x^2 + 6x + 6x + 9 - 6x - 9 = 0
    Combine like terms.
    4x2+6x+6x−6x+9−9=04x^2 + 6x + 6x - 6x + 9 - 9 = 0
    4x2+6x=04x^2 + 6x = 0
  3. Combine Like Terms: Factor out the common term xx from the equation.\newlinex(4x+6)=0x(4x + 6) = 0
  4. Factor Out Common Term: Apply the zero-product property to find the values of xx.x=0x = 0 or 4x+6=04x + 6 = 0
  5. Apply Zero-Product Property: Solve the second equation for x.\newline4x+6=04x + 6 = 0\newlineSubtract 66 from both sides.\newline4x=−64x = -6\newlineDivide both sides by 44.\newlinex=−64x = \frac{-6}{4}\newlineSimplify the fraction.\newlinex=−32x = \frac{-3}{2}

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