Solve Using the Square Root Property 4x^2-14=0

Math
4×2-14=0
Add 14 to both sides of the equation.
4×2=14
Divide each term by 4 and simplify.
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Divide each term in 4×2=14 by 4.
4×24=144
Cancel the common factor of 4.
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Cancel the common factor.
4×24=144
Divide x2 by 1.
x2=144
x2=144
Cancel the common factor of 14 and 4.
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Factor 2 out of 14.
x2=2(7)4
Cancel the common factors.
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Factor 2 out of 4.
x2=2⋅72⋅2
Cancel the common factor.
x2=2⋅72⋅2
Rewrite the expression.
x2=72
x2=72
x2=72
x2=72
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x=±72
The complete solution is the result of both the positive and negative portions of the solution.
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Simplify the right side of the equation.
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Rewrite 72 as 72.
x=±72
Multiply 72 by 22.
x=±72⋅22
Combine and simplify the denominator.
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Multiply 72 and 22.
x=±7222
Raise 2 to the power of 1.
x=±7222
Raise 2 to the power of 1.
x=±7222
Use the power rule aman=am+n to combine exponents.
x=±7221+1
Add 1 and 1.
x=±7222
Rewrite 22 as 2.
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Use axn=axn to rewrite 2 as 212.
x=±72(212)2
Apply the power rule and multiply exponents, (am)n=amn.
x=±72212⋅2
Combine 12 and 2.
x=±72222
Cancel the common factor of 2.
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Cancel the common factor.
x=±72222
Divide 1 by 1.
x=±722
x=±722
Evaluate the exponent.
x=±722
x=±722
x=±722
Simplify the numerator.
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Combine using the product rule for radicals.
x=±7⋅22
Multiply 7 by 2.
x=±142
x=±142
x=±142
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the ± to find the first solution.
x=142
Next, use the negative value of the ± to find the second solution.
x=-142
The complete solution is the result of both the positive and negative portions of the solution.
x=142,-142
x=142,-142
x=142,-142
The result can be shown in multiple forms.
Exact Form:
x=142,-142
Decimal Form:
x=1.87082869…,-1.87082869…
Solve Using the Square Root Property 4x^2-14=0

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