# Solve Using the Square Root Property 4x^2+7x=5x-5

4×2+7x=5x-5
Move all terms containing x to the left side of the equation.
Subtract 5x from both sides of the equation.
4×2+7x-5x=-5
Subtract 5x from 7x.
4×2+2x=-5
4×2+2x=-5
Move 5 to the left side of the equation by adding it to both sides.
4×2+2x+5=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=2, and c=5 into the quadratic formula and solve for x.
-2±22-4⋅(4⋅5)2⋅4
Simplify.
Simplify the numerator.
Raise 2 to the power of 2.
x=-2±4-4⋅(4⋅5)2⋅4
Multiply 4 by 5.
x=-2±4-4⋅202⋅4
Multiply -4 by 20.
x=-2±4-802⋅4
Subtract 80 from 4.
x=-2±-762⋅4
Rewrite -76 as -1(76).
x=-2±-1⋅762⋅4
Rewrite -1(76) as -1⋅76.
x=-2±-1⋅762⋅4
Rewrite -1 as i.
x=-2±i⋅762⋅4
Rewrite 76 as 22⋅19.
Factor 4 out of 76.
x=-2±i⋅4(19)2⋅4
Rewrite 4 as 22.
x=-2±i⋅22⋅192⋅4
x=-2±i⋅22⋅192⋅4
Pull terms out from under the radical.
x=-2±i⋅(219)2⋅4
Move 2 to the left of i.
x=-2±2i192⋅4
x=-2±2i192⋅4
Multiply 2 by 4.
x=-2±2i198
Simplify -2±2i198.
x=-1±i194
x=-1±i194
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 2 to the power of 2.
x=-2±4-4⋅(4⋅5)2⋅4
Multiply 4 by 5.
x=-2±4-4⋅202⋅4
Multiply -4 by 20.
x=-2±4-802⋅4
Subtract 80 from 4.
x=-2±-762⋅4
Rewrite -76 as -1(76).
x=-2±-1⋅762⋅4
Rewrite -1(76) as -1⋅76.
x=-2±-1⋅762⋅4
Rewrite -1 as i.
x=-2±i⋅762⋅4
Rewrite 76 as 22⋅19.
Factor 4 out of 76.
x=-2±i⋅4(19)2⋅4
Rewrite 4 as 22.
x=-2±i⋅22⋅192⋅4
x=-2±i⋅22⋅192⋅4
Pull terms out from under the radical.
x=-2±i⋅(219)2⋅4
Move 2 to the left of i.
x=-2±2i192⋅4
x=-2±2i192⋅4
Multiply 2 by 4.
x=-2±2i198
Simplify -2±2i198.
x=-1±i194
Change the ± to +.
x=-1+i194
Rewrite -1 as -1(1).
x=-1⋅1+i194
Factor -1 out of i19.
x=-1⋅1-(-i19)4
Factor -1 out of -1(1)-(-i19).
x=-1(1-i19)4
Move the negative in front of the fraction.
x=-1-i194
x=-1-i194
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 2 to the power of 2.
x=-2±4-4⋅(4⋅5)2⋅4
Multiply 4 by 5.
x=-2±4-4⋅202⋅4
Multiply -4 by 20.
x=-2±4-802⋅4
Subtract 80 from 4.
x=-2±-762⋅4
Rewrite -76 as -1(76).
x=-2±-1⋅762⋅4
Rewrite -1(76) as -1⋅76.
x=-2±-1⋅762⋅4
Rewrite -1 as i.
x=-2±i⋅762⋅4
Rewrite 76 as 22⋅19.
Factor 4 out of 76.
x=-2±i⋅4(19)2⋅4
Rewrite 4 as 22.
x=-2±i⋅22⋅192⋅4
x=-2±i⋅22⋅192⋅4
Pull terms out from under the radical.
x=-2±i⋅(219)2⋅4
Move 2 to the left of i.
x=-2±2i192⋅4
x=-2±2i192⋅4
Multiply 2 by 4.
x=-2±2i198
Simplify -2±2i198.
x=-1±i194
Change the ± to -.
x=-1-i194
Rewrite -1 as -1(1).
x=-1⋅1-i194
Factor -1 out of -i19.
x=-1⋅1-(i19)4
Factor -1 out of -1(1)-(i19).
x=-1(1+i19)4
Move the negative in front of the fraction.
x=-1+i194
x=-1+i194
The final answer is the combination of both solutions.
x=-1-i194,-1+i194
Solve Using the Square Root Property 4x^2+7x=5x-5