Solve the equation 2, x, squared, minus, 19, x, plus, 2, equals, minus, 10, x2x 2 −19x+2=−10x to the nearest tenth.
Question
Solve the equation 2, x, squared, minus, 19, x, plus, 2, equals, minus, 10, x2x 2 −19x+2=−10x to the nearest tenth.
Solution 1
The equation you provided seems to be a bit unclear. However, if you're asking to solve the quadratic equation 2x^2 - 19x + 2 = -10x, here are the steps:
First, we need to rearrange the equation to the standard form of a quadratic equation, which is ax^2 + bx + c = 0.
So, we add 10x to both sides of the equation to get:
2x^2 - 19x + 10x + 2 = 0
This simplifies to:
2x^2 - 9x + 2 = 0
Next, we can solve for x using the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a).
In this equation, a = 2, b = -9, and c = 2.
Substituting these values into the quadratic formula gives:
x = [9 ± sqrt((-9)^2 - 422)] / (2*2)
This simplifies to:
x = [9 ± sqrt(81 - 16)] / 4
Further simplification gives:
x = [9 ± sqrt(65)] / 4
So, the solutions to the equation are:
x = (9 + sqrt(65)) / 4 and x = (9 - sqrt(65)) / 4
To the nearest tenth, these are approximately x = 3.5 and x = 0.1.
Solution 2
The equation you provided seems to be a bit unclear, but I'm assuming you're asking to solve the quadratic equation 2x^2 - 19x + 2 = -10x.
First, let's simplify the equation by adding 10x to both sides to set the equation to zero:
2x^2 - 19x + 10x + 2 = 0
This simplifies to:
2x^2 - 9x + 2 = 0
Next, we can solve this quadratic equation using the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 2, b = -9, and c = 2.
Substituting these values into the quadratic formula gives:
x = [9 ± sqrt((-9)^2 - 422)] / (2*2) x = [9 ± sqrt(81 - 16)] / 4 x = [9 ± sqrt(65)] / 4
So the solutions to the equation are:
x = (9 + sqrt(65)) / 4 x = (9 - sqrt(65)) / 4
To the nearest tenth, these are approximately x = 2.8 and x = 0.2.
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