Solve by completing the square.x2+8x=29Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.x=_____ or x=_____
Q. Solve by completing the square.x2+8x=29Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.x=_____ or x=_____
Write Equation Form: Write the equation in the form of x2+bx=c. We have the equation x2+8x=29.
Complete Square:Complete the square by adding (2b)2 to both sides of the equation.Since (28)2=16, we add 16 to both sides to complete the square.x2+8x+16=29+16x2+8x+16=45
Factor Left Side: Factor the left side of the equation.The left side is a perfect square trinomial.(x+4)2=45
Take Square Root: Take the square root of both sides of the equation.(x+4)2=±45x+4=±45
Solve for x: Solve for x by isolating the variable.Subtract 4 from both sides of the equation.x=−4±45
Simplify Square Root: Simplify the square root and round to the nearest hundredth if necessary.45 is approximately 6.71.x=−4±6.71
Find Values of x: Find the two values of x.x≈−4+6.71 implies x≈2.71.x≈−4−6.71 implies x≈−10.71.Values of x: 2.71, −10.71
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