Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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x1=−163,x2=203
Alternative Form
x1=−0.1875,x2=0.15
Evaluate
(2x−3)2=(2x×9)2
Simplify
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Evaluate
(2x×9)2
Multiply the terms
(18x)2
To raise a product to a power,raise each factor to that power
182x2
Evaluate the power
324x2
(2x−3)2=324x2
Expand the expression
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Evaluate
(2x−3)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(2x)2−2×2x×3+32
Calculate
4x2−12x+9
4x2−12x+9=324x2
Move the expression to the left side
−320x2−12x+9=0
Factor the expression
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Evaluate
−320x2−12x+9
Rewrite the expression
−320x2+(48−60)x+9
Calculate
−320x2+48x−60x+9
Rewrite the expression
−16x×20x+16x×3−3×20x+3×3
Factor out −16x from the expression
−16x(20x−3)−3×20x+3×3
Factor out −3 from the expression
−16x(20x−3)−3(20x−3)
Factor out 20x−3 from the expression
(−16x−3)(20x−3)
(−16x−3)(20x−3)=0
When the product of factors equals 0,at least one factor is 0
20x−3=0−16x−3=0
Solve the equation for x
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Evaluate
20x−3=0
Move the constant to the right-hand side and change its sign
20x=0+3
Removing 0 doesn't change the value,so remove it from the expression
20x=3
Divide both sides
2020x=203
Divide the numbers
x=203
x=203−16x−3=0
Solve the equation for x
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Evaluate
−16x−3=0
Move the constant to the right-hand side and change its sign
−16x=0+3
Removing 0 doesn't change the value,so remove it from the expression
−16x=3
Change the signs on both sides of the equation
16x=−3
Divide both sides
1616x=16−3
Divide the numbers
x=16−3
Use b−a=−ba=−ba to rewrite the fraction
x=−163
x=203x=−163
Solution
x1=−163,x2=203
Alternative Form
x1=−0.1875,x2=0.15
Show Solution
