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Solve for x. x^(2)-20 x+100=0 x=

Solve for xx.\newlinex2−20x+100=0x^{2}-20x+100=0\newlinex=x=

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Full solution

Q. Solve for xx.\newlinex2−20x+100=0x^{2}-20x+100=0\newlinex=x=
  1. Identify Equation Type: Identify the type of equation and look for patterns.\newlineThe equation x2−20x+100=0x^2 - 20x + 100 = 0 is a quadratic equation in the form of ax2+bx+c=0ax^2 + bx + c = 0.\newlineNotice that the equation can be factored because 100100 is a perfect square and 20x20x is twice the product of the square root of 100100 and xx.
  2. Factor Quadratic Equation: Factor the quadratic equation.\newlinex2−20x+100=(x−10)(x−10)=0x^2 - 20x + 100 = (x - 10)(x - 10) = 0\newlineThis is because (x−10)2=x2−20x+100(x - 10)^2 = x^2 - 20x + 100.
  3. Solve for x: Solve for x by setting each factor equal to zero.\newlineSince (x−10)(x−10)=0(x - 10)(x - 10) = 0, we have x−10=0x - 10 = 0.
  4. Find x Value: Find the value of x.\newlinex−10=0x - 10 = 0 implies that x=10x = 10.

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