Solve by completing the square.m2−10m−29=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.`m` = ____ or `m` = _____
Q. Solve by completing the square.m2−10m−29=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.`m` = ____ or `m` = _____
Move constant term: We start with the equation m2−10m−29=0 and move the constant term to the right side of the equation.m2−10m=29
Complete the square: To complete the square, we need to add (2b)2 to both sides of the equation, where b is the coefficient of m. In this case, b=−10, so (2b)2=(2−10)2=25.m2−10m+25=29+25
Simplify equation: Simplify both sides of the equation. m2−10m+25=54
Factor perfect square trinomial: Now, the left side of the equation is a perfect square trinomial, which can be factored into (m−5)2.(m−5)2=54
Take square root: Take the square root of both sides of the equation to solve for m.m−5=±54
Simplify square root: Simplify the square root of 54. Since 54=9×6 and 9=3, we have 54=9×6=36.m−5=±36
Isolate m: Add 5 to both sides of the equation to isolate m.m=5±36
Express as decimals: Now we can express the solutions as decimals rounded to the nearest hundredth. 6 is approximately 2.45, so 36 is approximately 3×2.45=7.35.m≈5±7.35
Calculate values: Calculate the two possible values for m.m≈5+7.35≈12.35m≈5−7.35≈−2.35
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