Solve Using the Square Root Property 7x^2+3=8x

Math
7×2+3=8x
Subtract 8x from both sides of the equation.
7×2+3-8x=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=7, b=-8, and c=3 into the quadratic formula and solve for x.
8±(-8)2-4⋅(7⋅3)2⋅7
Simplify.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(7⋅3)2⋅7
Multiply 7 by 3.
x=8±64-4⋅212⋅7
Multiply -4 by 21.
x=8±64-842⋅7
Subtract 84 from 64.
x=8±-202⋅7
Rewrite -20 as -1(20).
x=8±-1⋅202⋅7
Rewrite -1(20) as -1⋅20.
x=8±-1⋅202⋅7
Rewrite -1 as i.
x=8±i⋅202⋅7
Rewrite 20 as 22⋅5.
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Factor 4 out of 20.
x=8±i⋅4(5)2⋅7
Rewrite 4 as 22.
x=8±i⋅22⋅52⋅7
x=8±i⋅22⋅52⋅7
Pull terms out from under the radical.
x=8±i⋅(25)2⋅7
Move 2 to the left of i.
x=8±2i52⋅7
x=8±2i52⋅7
Multiply 2 by 7.
x=8±2i514
Simplify 8±2i514.
x=4±i57
x=4±i57
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(7⋅3)2⋅7
Multiply 7 by 3.
x=8±64-4⋅212⋅7
Multiply -4 by 21.
x=8±64-842⋅7
Subtract 84 from 64.
x=8±-202⋅7
Rewrite -20 as -1(20).
x=8±-1⋅202⋅7
Rewrite -1(20) as -1⋅20.
x=8±-1⋅202⋅7
Rewrite -1 as i.
x=8±i⋅202⋅7
Rewrite 20 as 22⋅5.
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Factor 4 out of 20.
x=8±i⋅4(5)2⋅7
Rewrite 4 as 22.
x=8±i⋅22⋅52⋅7
x=8±i⋅22⋅52⋅7
Pull terms out from under the radical.
x=8±i⋅(25)2⋅7
Move 2 to the left of i.
x=8±2i52⋅7
x=8±2i52⋅7
Multiply 2 by 7.
x=8±2i514
Simplify 8±2i514.
x=4±i57
Change the ± to +.
x=4+i57
x=4+i57
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -8 to the power of 2.
x=8±64-4⋅(7⋅3)2⋅7
Multiply 7 by 3.
x=8±64-4⋅212⋅7
Multiply -4 by 21.
x=8±64-842⋅7
Subtract 84 from 64.
x=8±-202⋅7
Rewrite -20 as -1(20).
x=8±-1⋅202⋅7
Rewrite -1(20) as -1⋅20.
x=8±-1⋅202⋅7
Rewrite -1 as i.
x=8±i⋅202⋅7
Rewrite 20 as 22⋅5.
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Factor 4 out of 20.
x=8±i⋅4(5)2⋅7
Rewrite 4 as 22.
x=8±i⋅22⋅52⋅7
x=8±i⋅22⋅52⋅7
Pull terms out from under the radical.
x=8±i⋅(25)2⋅7
Move 2 to the left of i.
x=8±2i52⋅7
x=8±2i52⋅7
Multiply 2 by 7.
x=8±2i514
Simplify 8±2i514.
x=4±i57
Change the ± to -.
x=4-i57
x=4-i57
The final answer is the combination of both solutions.
x=4+i57,4-i57
Solve Using the Square Root Property 7x^2+3=8x

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