Algebra
Calculus
Trigonometry
Matrix
Question
Solve the quadratic equation
Solve by factoring
Solve using the quadratic formula
Solve by completing the square
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x1=−25,x2=2
Alternative Form
x1=−2.5,x2=2
Evaluate
(x−2)(3x+5)=x(x−2)
Expand the expression
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Evaluate
(x−2)(3x+5)
Apply the distributive property
x×3x+x×5−2×3x−2×5
Multiply the terms
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Evaluate
x×3x
Use the commutative property to reorder the terms
3x×x
Multiply the terms
3x2
3x2+x×5−2×3x−2×5
Use the commutative property to reorder the terms
3x2+5x−2×3x−2×5
Multiply the numbers
3x2+5x−6x−2×5
Multiply the numbers
3x2+5x−6x−10
Subtract the terms
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Evaluate
5x−6x
Collect like terms by calculating the sum or difference of their coefficients
(5−6)x
Subtract the numbers
−x
3x2−x−10
3x2−x−10=x(x−2)
Expand the expression
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Evaluate
x(x−2)
Apply the distributive property
x×x−x×2
Multiply the terms
x2−x×2
Use the commutative property to reorder the terms
x2−2x
3x2−x−10=x2−2x
Move the expression to the left side
2x2+x−10=0
Factor the expression
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Evaluate
2x2+x−10
Rewrite the expression
2x2+(5−4)x−10
Calculate
2x2+5x−4x−10
Rewrite the expression
x×2x+x×5−2×2x−2×5
Factor out x from the expression
x(2x+5)−2×2x−2×5
Factor out −2 from the expression
x(2x+5)−2(2x+5)
Factor out 2x+5 from the expression
(x−2)(2x+5)
(x−2)(2x+5)=0
When the product of factors equals 0,at least one factor is 0
x−2=02x+5=0
Solve the equation for x
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=22x+5=0
Solve the equation for x
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Evaluate
2x+5=0
Move the constant to the right-hand side and change its sign
2x=0−5
Removing 0 doesn't change the value,so remove it from the expression
2x=−5
Divide both sides
22x=2−5
Divide the numbers
x=2−5
Use b−a=−ba=−ba to rewrite the fraction
x=−25
x=2x=−25
Solution
x1=−25,x2=2
Alternative Form
x1=−2.5,x2=2
Show Solution
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