Answer:
Step-by-step explanation:
Given
Required
Solve for x
Subtract 5 from both sides
Divide through by 3
If the quadratic formula is used to solve 2x2 = 8x -3, what are the solutions
2 answers:
Answer:
x = 2 ±
Step-by-step explanation:
Given a quadratic equation in standard form : ax² + bx + c = 0
Then we can solve for x using the quadratic formula
Given
2x² = 8x - 3 ( subtract 8x - 3 from both sides )
2x² - 8x + 3 = 0 ← in standard form
with a = 2, b = - 8 and c = 3, hence
x = (- (- 8) ± ) / 4
= (8 ± ) / 4
= (8 ± ) / 4
= (8 ± 2 ) / 4
= ±
= 2 ±
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In these questions, we need to follow the steps:
1 - solve for the trigonometric function
2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.
3 - Complete these angles with the complete round repetition, by adding
4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.
1 - To solve, we just use algebraic operations:
2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:
The value for the angle that give positive
is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of
Are:
3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:
Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:
4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:
So, the solutions are:
