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Simplifying a2 + -410a + 21 = 0 Reorder the terms: 21 + -410a + a2 = 0 Solving 21 + -410a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -410a + -21 + a2 = 0 + -21 Reorder the terms: 21 + -21 + -410a + a2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -410a + a2 = 0 + -21 -410a + a2 = 0 + -21 Combine like terms: 0 + -21 = -21 -410a + a2 = -21 The a term is -410a. Take half its coefficient (-205). Square it (42025) and add it to both sides. Add '42025' to each side of the equation. -410a + 42025 + a2 = -21 + 42025 Reorder the terms: 42025 + -410a + a2 = -21 + 42025 Combine like terms: -21 + 42025 = 42004 42025 + -410a + a2 = 42004 Factor a perfect square on the left side: (a + -205)(a + -205) = 42004 Calculate the square root of the right side: 204.948774088 Break this problem into two subproblems by setting (a + -205) equal to 204.948774088 and -204.948774088.Subproblem 1
a + -205 = 204.948774088 Simplifying a + -205 = 204.948774088 Reorder the terms: -205 + a = 204.948774088 Solving -205 + a = 204.948774088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '205' to each side of the equation. -205 + 205 + a = 204.948774088 + 205 Combine like terms: -205 + 205 = 0 0 + a = 204.948774088 + 205 a = 204.948774088 + 205 Combine like terms: 204.948774088 + 205 = 409.948774088 a = 409.948774088 Simplifying a = 409.948774088Subproblem 2
a + -205 = -204.948774088 Simplifying a + -205 = -204.948774088 Reorder the terms: -205 + a = -204.948774088 Solving -205 + a = -204.948774088 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '205' to each side of the equation. -205 + 205 + a = -204.948774088 + 205 Combine like terms: -205 + 205 = 0 0 + a = -204.948774088 + 205 a = -204.948774088 + 205 Combine like terms: -204.948774088 + 205 = 0.051225912 a = 0.051225912 Simplifying a = 0.051225912Solution
The solution to the problem is based on the solutions from the subproblems. a = {409.948774088, 0.051225912}
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