(х+2)²+2(х+2)-3=0

Question 1

Задача Задача №89818

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Аноним

06 декабря 2023 07:13 · публичный вопрос

А

Аноним 06 декабря 2023 07:13

(х+2)²+2(х+2)-3=0

Answer

To solve the equation (х+2)²+2(х+2)-3=0, we can use the quadratic formula.

The quadratic formula is given by x = (-b ± √(b²-4ac)) / (2a), where ax² + bx + c = 0 is a quadratic equation.

Comparing the given equation to the standard form, we have: a = 1 b = 2(х+2) c = -3

Substituting these values into the quadratic formula, we get: x = (-2(х+2) ± √((2(х+2))² - 4(1)(-3))) / (2(1))

Simplifying further: x = (-2x - 4 ± √(4(x+2)² + 12)) / 2

Now, let's expand and simplify the expression within the square root: x = (-2x - 4 ± √(4(x² + 4x + 4) + 12)) / 2 x = (-2x - 4 ± √(4x² + 16x + 16 + 12)) / 2 x = (-2x - 4 ± √(4x² + 16x + 28)) / 2 x = (-2x - 4 ± 2√(x² + 4x + 7)) / 2

Next, we can simplify further: x = -x - 2 ± √(x² + 4x + 7) / 2 x = (-x - 2 ± √(x² + 4x + 7)) / 2

So, the solutions to the equation (х+2)²+2(х+2)-3=0 are given by x = (-x - 2 ± √(x² + 4x + 7)) / 2.

Question 2

(х+2)²+2(х+2)-3=0

Answer

To solve the equation (х+2)²+2(х+2)-3=0, we can use the quadratic formula. The quadratic formula is given by x = (-b ± √(b²-4ac)) / (2a), where ax² + bx + c = 0 is a quadratic equation. Comparing the given equation to the standard form, we have: a = 1 b = 2(х+2) c = -3 Substituting these values into the quadratic formula, we get: x = (-2(х+2) ± √((2(х+2))² - 4(1)(-3))) / (2(1)) Simplifying further: x = (-2x - 4 ± √(4(x+2)² + 12)) / 2 Now, let's expand and simplify the expression within the square root: x = (-2x - 4 ± √(4(x² + 4x + 4) + 12)) / 2 x = (-2x - 4 ± √(4x² + 16x + 16 + 12)) / 2 x = (-2x - 4 ± √(4x² + 16x + 28)) / 2 x = (-2x - 4 ± 2√(x² + 4x + 7)) / 2 Next, we can simplify further: x = -x - 2 ± √(x² + 4x + 7) / 2 x = (-x - 2 ± √(x² + 4x + 7)) / 2 So, the solutions to the equation (х+2)²+2(х+2)-3=0 are given by x = (-x - 2 ± √(x² + 4x + 7)) / 2.