Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=2−22,x2=2+22
Alternative Form
x1≈−0.828427,x2≈4.828427
Evaluate
3(x−2)2=24
Expand the expression
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Evaluate
3(x−2)2
Expand the expression
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Evaluate
(x−2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×2+22
Calculate
x2−4x+4
3(x2−4x+4)
Apply the distributive property
3x2−3×4x+3×4
Multiply the numbers
3x2−12x+3×4
Multiply the numbers
3x2−12x+12
3x2−12x+12=24
Move the expression to the left side
3x2−12x−12=0
Substitute a=3,b=−12 and c=−12 into the quadratic formula x=2a−b±b2−4ac
x=2×312±(−12)2−4×3(−12)
Simplify the expression
x=612±(−12)2−4×3(−12)
Simplify the expression
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Evaluate
(−12)2−4×3(−12)
Multiply
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Multiply the terms
4×3(−12)
Rewrite the expression
−4×3×12
Multiply the terms
−144
(−12)2−(−144)
Rewrite the expression
122−(−144)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
122+144
Evaluate the power
144+144
Add the numbers
288
x=612±288
Simplify the radical expression
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Evaluate
288
Write the expression as a product where the root of one of the factors can be evaluated
144×2
Write the number in exponential form with the base of 12
122×2
The root of a product is equal to the product of the roots of each factor
122×2
Reduce the index of the radical and exponent with 2
122
x=612±122
Separate the equation into 2 possible cases
x=612+122x=612−122
Simplify the expression
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Evaluate
x=612+122
Divide the terms
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Evaluate
612+122
Rewrite the expression
66(2+22)
Reduce the fraction
2+22
x=2+22
x=2+22x=612−122
Simplify the expression
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Evaluate
x=612−122
Divide the terms
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Evaluate
612−122
Rewrite the expression
66(2−22)
Reduce the fraction
2−22
x=2−22
x=2+22x=2−22
Solution
x1=2−22,x2=2+22
Alternative Form
x1≈−0.828427,x2≈4.828427
Show Solution
