Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 + 2x = 17
1 answer:
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Equation Given
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x² + 2x = 17
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Add the constant to make it perfect square
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x² + 2x + (2/2)² - ²(2/2)² = 17
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Evaluate the brackets
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x² + 2x + (1)² - ²(1)² = 17
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Form the perfect square
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(x + 1)² - 1 = 17
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Add 1 to both sides
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(x + 1)² = 17 + 1
(x + 1)² = 18
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Square root both sides
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√(x + 1)² =
√18
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Solve for x
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x = 4.24 - 1 or - 4.24 -1
x = 3.24 or - 5.24 (nearest hundredth)
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Answer: x = x = 3.24 or - 5.24
--------------------------------------------------------
Equation Given
--------------------------------------------------------
x² + 2x = 17
--------------------------------------------------------
Add the constant to make it perfect square
--------------------------------------------------------
x² + 2x + (2/2)² - ²(2/2)² = 17
--------------------------------------------------------
Evaluate the brackets
--------------------------------------------------------
x² + 2x + (1)² - ²(1)² = 17
--------------------------------------------------------
Form the perfect square
--------------------------------------------------------
(x + 1)² - 1 = 17
--------------------------------------------------------
Add 1 to both sides
--------------------------------------------------------
(x + 1)² = 17 + 1
(x + 1)² = 18
--------------------------------------------------------
Square root both sides
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√(x + 1)² =
--------------------------------------------------------
Solve for x
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x = 4.24 - 1 or - 4.24 -1
x = 3.24 or - 5.24 (nearest hundredth)
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Answer: x = x = 3.24 or - 5.24
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To calculate it use pythagoras: a^2+b^2=c^2
7^2+10^2=49+100=149
calculate the square root:
so the diagonal is about 12.2 inches long
7^2+10^2=49+100=149
calculate the square root:
so the diagonal is about 12.2 inches long