Solve (x-2) (x+5) +12 = (x+3) (x-4) -2 and check the solution
Answers
Let's solve your equation step-by-step.
(x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
Step 1: Multiply the binomial to the binomial in the LHS as well as RHS.
⇒ (x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
⇒ x (x + 5) - 2 (x + 5) + 12 = x (x - 4) + 3 (x - 4) - 2
⇒ x (x) + x (5) - 2 (x) - 2 (5) + 12 = x (x) - x (4) + 3 (x) - 3 (4) - 2
⇒ x² + 5x - 2x - 10 + 12 = x² - 4x + 3x - 12 - 2
Step 2: Combine like terms and solve.
⇒ x² + 5x - 2x - 10 + 12 = x² - 4x + 3x - 12 - 2
⇒ x² + 3x + 2 = x² - x - 14
Step 3: Subtract 2 to both sides of the equation.
⇒ x² + 3x + 2 - 2 = x² - x - 14 - 2
⇒ x² + 3x = x² - x - 16
Step 4: Add x from both sides of the equation.
⇒ x² + 3x + x = x² - x - 16 + x
⇒ x² + 4x = x² - 16
Step 5: Subtract x² from both sides of the equation.
⇒ x² + 4x - x² = x² - 16 - x²
⇒ 4x = -16
Step 6: Divide 4 from both sides of the equation.
⇒ 4x ÷ 4 = -16 ÷ 4
⇒ x = -4
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Verification if the value of 'x' is -4
⇒ (x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
⇒ (-4 - 2) (-4 + 5) + 12 = (-4 + 3) (-4 - 4) - 2
⇒ -6 (1) + 12 = - 1 (- 8) - 2
⇒ -6 + 12 = 8 - 2
⇒ 6 = 6
∴ x = -4 in the equation → (x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
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✮ Question : Solve for x in (x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
✮ Given : (x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
✮ To Find : Value of x
✮ Answer : x = -4
✮ Explanation :
(x - 2) (x + 5) + 12 = (x + 3) (x - 4) - 2
⇒ x² + 3x - 10 + 12 = (x + 3) (x - 4) - 2
⇒ x² + 3x + 2 = (x + 3) (x - 4) - 2
⇒ x² + 3x + 2 = x² - x - 14
Subtract 2 from both sides
⇒ x² + 3x + 2 - 2 = x² - x - 14 - 2
⇒ x² + 3x = x² - x - 16
Subtract x² - x from both sides
⇒ x² + 3x - (x² - x) = x² - x - 16 - (x² - x)
⇒ x² + 3x - x² + x = x² - x - 16 - x² + x
⇒ 3x + x = -16
⇒ 4x = -16
Dividing both sides by 4
⇒ 4x/4 = -16/4
⇒ x = -4