Solve Using the Square Root Property 24x^2+46x-55=10

24×2+46x-55=10
Move all terms to the left side of the equation and simplify.
Move 10 to the left side of the equation by subtracting it from both sides.
24×2+46x-55-10=0
Subtract 10 from -55.
24×2+46x-65=0
24×2+46x-65=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=24, b=46, and c=-65 into the quadratic formula and solve for x.
-46±462-4⋅(24⋅-65)2⋅24
Simplify.
Simplify the numerator.
Raise 46 to the power of 2.
x=-46±2116-4⋅(24⋅-65)2⋅24
Multiply 24 by -65.
x=-46±2116-4⋅-15602⋅24
Multiply -4 by -1560.
x=-46±2116+62402⋅24
x=-46±83562⋅24
Rewrite 8356 as 22⋅2089.
Factor 4 out of 8356.
x=-46±4(2089)2⋅24
Rewrite 4 as 22.
x=-46±22⋅20892⋅24
x=-46±22⋅20892⋅24
Pull terms out from under the radical.
x=-46±220892⋅24
x=-46±220892⋅24
Multiply 2 by 24.
x=-46±2208948
Simplify -46±2208948.
x=-23±208924
x=-23±208924
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise 46 to the power of 2.
x=-46±2116-4⋅(24⋅-65)2⋅24
Multiply 24 by -65.
x=-46±2116-4⋅-15602⋅24
Multiply -4 by -1560.
x=-46±2116+62402⋅24
x=-46±83562⋅24
Rewrite 8356 as 22⋅2089.
Factor 4 out of 8356.
x=-46±4(2089)2⋅24
Rewrite 4 as 22.
x=-46±22⋅20892⋅24
x=-46±22⋅20892⋅24
Pull terms out from under the radical.
x=-46±220892⋅24
x=-46±220892⋅24
Multiply 2 by 24.
x=-46±2208948
Simplify -46±2208948.
x=-23±208924
Change the ± to +.
x=-23+208924
Rewrite -23 as -1(23).
x=-1⋅23+208924
Factor -1 out of 2089.
x=-1⋅23-1(-2089)24
Factor -1 out of -1(23)-1(-2089).
x=-1(23-2089)24
Move the negative in front of the fraction.
x=-23-208924
x=-23-208924
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise 46 to the power of 2.
x=-46±2116-4⋅(24⋅-65)2⋅24
Multiply 24 by -65.
x=-46±2116-4⋅-15602⋅24
Multiply -4 by -1560.
x=-46±2116+62402⋅24
x=-46±83562⋅24
Rewrite 8356 as 22⋅2089.
Factor 4 out of 8356.
x=-46±4(2089)2⋅24
Rewrite 4 as 22.
x=-46±22⋅20892⋅24
x=-46±22⋅20892⋅24
Pull terms out from under the radical.
x=-46±220892⋅24
x=-46±220892⋅24
Multiply 2 by 24.
x=-46±2208948
Simplify -46±2208948.
x=-23±208924
Change the ± to -.
x=-23-208924
Rewrite -23 as -1(23).
x=-1⋅23-208924
Factor -1 out of -2089.
x=-1⋅23-(2089)24
Factor -1 out of -1(23)-(2089).
x=-1(23+2089)24
Move the negative in front of the fraction.
x=-23+208924
x=-23+208924
The final answer is the combination of both solutions.
x=-23-208924,-23+208924
The result can be shown in multiple forms.
Exact Form:
x=-23-208924,-23+208924
Decimal Form:
x=0.94606581…,-2.86273248…
Solve Using the Square Root Property 24x^2+46x-55=10