Question

Solve the quadratic equation 49-(x-3)2 =0.​

Answer 1

Method 1 → Solve with Quadratic Formula

Let's solve your equation step-by-step.

49 - (x - 3)² = 0

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Step 1: Simplify both sides of the equation.

-x² + 6x + 40 = 0

For this equation: a = -1, b = 6, c = 40

-1x² + 6x + 40 = 0

Step 2: Use quadratic formula with a = -1, b = 6, c = 40.

⇒ $\sf \dfrac{-b\± \sqrt{b^{2} - 4ac} }{2a}$

⇒ $\sf \dfrac{-6\± \sqrt{6^{2} - 4(-1)(40) }}{2(-1)}$

⇒ $\sf \dfrac{-6\± \sqrt{36 - (-160) }}{2(-1)}$

⇒ $\sf \dfrac{-6\± \sqrt{36 +160 }}{2(-1)}$

⇒ $\sf \dfrac{-6\± \sqrt{196 }}{2(-1)}$

⇒ $\sf \dfrac{-6\± 14}{-2}$

⇒ $x = -4\ or \ x=10$

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Method 2 → Solve by Factoring

Let's solve your equation step-by-step.

49 - (x - 3)² = 0

Step 1: Simplify both sides of the equation.

-x² + 6x + 40 = 0

Step 2: Factor left side of equation.

(-x - 4) (x - 10) = 0

Step 3: Set factors equal to 0.

-x - 4 = 0 or x - 10 = 0

x = - 4 or x = 10

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Method 3 → Solve by Completing Square

Let's solve your equation step-by-step.

49 - (x - 3)² = 0

Step 1: Simplify both sides of the equation.

-x² + 6x + 40 = 0

Step 2: Subtract 40 from both sides.

-x² + 6x + 40 - 40 = 0 - 40

-x² + 6x = -40

Step 3: Since the coefficient of -x² is -1, divide both sides by -1.

$\dfrac{-x^{2}+6x}{-1} = \dfrac{-40}{-1}$

x² - 6x = 40

Step 4: The coefficient of -6x is -6. Let b = -6.

Then we need to add $(\frac{b}{2})^{2} =9$ to both sides to complete the square.

Add 9 to both sides.

x² - 6x + 9 = 40 + 9

x² - 6x + 9 = 49

Step 5: Factor left side.

(x - 3)² = 49

Step 6: Take square root.

x - 3 = ± √49

Step 7: Add 3 to both sides.

x - 3 + 3 = 3 ± √49

x = 3 ± √49

x = 3 + 7 or x = 3 - 7

x = -4 or x = 10

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Answer 2

Answer:

Question

Solve the quadratic equation 49-(x-3)2 =0.

$\huge \bold {Solution}$

$49 - {(x - 3)}^{2} = 0$

Simplify the both sides

$-x² + 6x + 40 = 0$

Factor the left side of equation.

$\: (-x - 4) (x - 10) = 0$

Set factor = 0

$-x - 4 = 0 \: or \: x - 10 = 0</p><p></p><p>x = - 4 \: or \: x = 10</p><p></p><p>$

x = -4 or 10