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Simplifying 5a2 + -1a = 35 Reorder the terms: -1a + 5a2 = 35 Solving -1a + 5a2 = 35 Solving for variable 'a'. Reorder the terms: -35 + -1a + 5a2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -1a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + -0.2a + a2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.2a + 7 + a2 = 0 + 7 Reorder the terms: -7 + 7 + -0.2a + a2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.2a + a2 = 0 + 7 -0.2a + a2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.2a + a2 = 7 The a term is -0.2a. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2a + 0.01 + a2 = 7 + 0.01 Reorder the terms: 0.01 + -0.2a + a2 = 7 + 0.01 Combine like terms: 7 + 0.01 = 7.01 0.01 + -0.2a + a2 = 7.01 Factor a perfect square on the left side: (a + -0.1)(a + -0.1) = 7.01 Calculate the square root of the right side: 2.647640459 Break this problem into two subproblems by setting (a + -0.1) equal to 2.647640459 and -2.647640459.Subproblem 1
a + -0.1 = 2.647640459 Simplifying a + -0.1 = 2.647640459 Reorder the terms: -0.1 + a = 2.647640459 Solving -0.1 + a = 2.647640459 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = 2.647640459 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = 2.647640459 + 0.1 a = 2.647640459 + 0.1 Combine like terms: 2.647640459 + 0.1 = 2.747640459 a = 2.747640459 Simplifying a = 2.747640459Subproblem 2
a + -0.1 = -2.647640459 Simplifying a + -0.1 = -2.647640459 Reorder the terms: -0.1 + a = -2.647640459 Solving -0.1 + a = -2.647640459 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = -2.647640459 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = -2.647640459 + 0.1 a = -2.647640459 + 0.1 Combine like terms: -2.647640459 + 0.1 = -2.547640459 a = -2.547640459 Simplifying a = -2.547640459Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.747640459, -2.547640459}
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