Answer:
x² + 4x - 7 = (x + 2)² - 11
Step-by-step explanation:
Let us solve the question
∵ The expression is x² + 4x - 7
∵ The form is (x + a)² - b
→ To express the equation in the given form quate them
∴ x² + 4x - 7 = (x + a)² - b
→ Simplify the right side then equate the like terms to find a and b
∵ (x + a)² = (x + a)(x + a)
∴ (x + a)² = (x)(x) + (x)(a) + (a)(x) + (a)(a)
∴ (x + a)² = x² + ax + ax + a²
→ Add the like terms
∵ (x + a)² = x² + (ax + ax) + a²
∴ (x + a)² = x² + 2ax + a²
→ Substitute (x + a)² in the right side by x² + 2ax + a²
∵ x² + 4x - 7 = x² + 2ax + a² - b
→ Equate the coefficients of the like terms
∵ 4x and 2ax are like terms
∴ 4 = 2a
→ Divide both sides by 2
∴ 2 = a
∵ -7 and a² - b are like terms ⇒ constant terms
∴ -7 = a² - b
∵ a = 2
∴ -7 = (2)² - b
∴ -7 = 4 - b
→ Subtract 4 from both sides
∵ -7 - 4 = 4 - 4 - b
∴ -11 = -b
→ Divide both sides by -1
∴ 11 = b
→ Substitute the values of a and b in the given form
∴ (x + a)² - b = (x + 2)² - 11
∴ x² + 4x - 7 = (x + 2)² - 11
