Question

Find soluton to x^2-14x+49=25

Answer 1

$\boxed{x=12 \ and \ x=2}$

Explanation:

In this exercise, we have the following equation:

$x^2-14x+49=25$

We can write this Quadratic Equation in Standard Form as follows:

$x^2-14x+49=25 \\ \\ Subtract \ 25 \ from \ both \ sides: \\ \\ x^2-14x+49-25=25-25 \\ \\ x^2-14x+24=0$

So this is a Non-perfect Square Trinomial. To factor out this, let's choose two numbers such that:

• The sum is -14
• The product is 24

Those numbers are:

• -12 and -2
• SUM: -12-2 = -14
• PRODUCT: (-12)(-2)=24

So we can write this as:

$x^2 + (a + b)x + ab=(x + a)(x + b) \\ \\ a=-12 \\ b=-2 \\ \\ x^2-14x+24=(x-12)(x-2)=0 \\ \\ So \ the \ solutions \ are: \\ \\ \boxed{x=12 \ and \ x=2}$

Learn more:

Quadratic Ffrmua: brainly.com/question/10188317

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