Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x≈0.62401
Evaluate
3x2+55x−10=0
Find the domain
More Steps
Evaluate
5x≥0
Rewrite the expression
x≥0
3x2+55x−10=0,x≥0
Move the expression to the right-hand side and change its sign
55x=−3x2+10
Rewrite the expression
5x=5−3x2+10
Evaluate
5x=5−3x2+10,5−3x2+10≥0
Evaluate
More Steps
Evaluate
5−3x2+10≥0
Simplify
−3x2+10≥0
Move the constant to the right side
−3x2≥−10
Change the signs on both sides of the inequality and flip the inequality sign
3x2≤10
Divide both sides
33x2≤310
Divide the numbers
x2≤310
Take the 2-th root on both sides of the inequality
x2≤310
Calculate
∣x∣≤330
Separate the inequality into 2 possible cases
{x≤330x≥−330
Find the intersection
−330≤x≤330
5x=5−3x2+10,−330≤x≤330
Solve the equation for x
More Steps
Evaluate
5x=5−3x2+10
Raise both sides of the equation to the 2-th power to eliminate the isolated 2-th root
(5x)2=(5−3x2+10)2
Evaluate the power
5x=259x4−60x2+100
Cross multiply
5x×25=9x4−60x2+100
Simplify the equation
125x=9x4−60x2+100
Move the expression to the left side
125x−(9x4−60x2+100)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
125x−9x4+60x2−100=0
Calculate
x≈0.62401x≈3.154797
x≈0.62401x≈3.154797,−330≤x≤330
Find the intersection
x≈0.62401
Check if the solution is in the defined range
x≈0.62401,x≥0
Find the intersection of the solution and the defined range
x≈0.62401
Solution
x≈0.62401
Show Solution
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