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Simplifying 10 = 5a2 + 10a + 20 Reorder the terms: 10 = 20 + 10a + 5a2 Solving 10 = 20 + 10a + 5a2 Solving for variable 'a'. Combine like terms: 10 + -20 = -10 -10 + -10a + -5a2 = 20 + 10a + 5a2 + -20 + -10a + -5a2 Reorder the terms: -10 + -10a + -5a2 = 20 + -20 + 10a + -10a + 5a2 + -5a2 Combine like terms: 20 + -20 = 0 -10 + -10a + -5a2 = 0 + 10a + -10a + 5a2 + -5a2 -10 + -10a + -5a2 = 10a + -10a + 5a2 + -5a2 Combine like terms: 10a + -10a = 0 -10 + -10a + -5a2 = 0 + 5a2 + -5a2 -10 + -10a + -5a2 = 5a2 + -5a2 Combine like terms: 5a2 + -5a2 = 0 -10 + -10a + -5a2 = 0 Factor out the Greatest Common Factor (GCF), '-5'. -5(2 + 2a + a2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(2 + 2a + a2)' equal to zero and attempt to solve: Simplifying 2 + 2a + a2 = 0 Solving 2 + 2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 2a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2a + a2 = 0 + -2 2a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 2a + a2 = -2 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -2 + 1 Reorder the terms: 1 + 2a + a2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2a + a2 = -1 Factor a perfect square on the left side: (a + 1)(a + 1) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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