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Simplifying 25a2 + -15 = 2a Reorder the terms: -15 + 25a2 = 2a Solving -15 + 25a2 = 2a Solving for variable 'a'. Reorder the terms: -15 + -2a + 25a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -15 + -2a + 25a2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.6 + -0.08a + a2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.08a + 0.6 + a2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.08a + a2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.08a + a2 = 0 + 0.6 -0.08a + a2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.08a + a2 = 0.6 The a term is -0.08a. Take half its coefficient (-0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. -0.08a + 0.0016 + a2 = 0.6 + 0.0016 Reorder the terms: 0.0016 + -0.08a + a2 = 0.6 + 0.0016 Combine like terms: 0.6 + 0.0016 = 0.6016 0.0016 + -0.08a + a2 = 0.6016 Factor a perfect square on the left side: (a + -0.04)(a + -0.04) = 0.6016 Calculate the square root of the right side: 0.775628777 Break this problem into two subproblems by setting (a + -0.04) equal to 0.775628777 and -0.775628777.Subproblem 1
a + -0.04 = 0.775628777 Simplifying a + -0.04 = 0.775628777 Reorder the terms: -0.04 + a = 0.775628777 Solving -0.04 + a = 0.775628777 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + a = 0.775628777 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + a = 0.775628777 + 0.04 a = 0.775628777 + 0.04 Combine like terms: 0.775628777 + 0.04 = 0.815628777 a = 0.815628777 Simplifying a = 0.815628777Subproblem 2
a + -0.04 = -0.775628777 Simplifying a + -0.04 = -0.775628777 Reorder the terms: -0.04 + a = -0.775628777 Solving -0.04 + a = -0.775628777 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.04' to each side of the equation. -0.04 + 0.04 + a = -0.775628777 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + a = -0.775628777 + 0.04 a = -0.775628777 + 0.04 Combine like terms: -0.775628777 + 0.04 = -0.735628777 a = -0.735628777 Simplifying a = -0.735628777Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.815628777, -0.735628777}
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