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Simplifying 10a2 + -7a = 1 Reorder the terms: -7a + 10a2 = 1 Solving -7a + 10a2 = 1 Solving for variable 'a'. Reorder the terms: -1 + -7a + 10a2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -7a + 10a2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -0.7a + a2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.7a + 0.1 + a2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.7a + a2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.7a + a2 = 0 + 0.1 -0.7a + a2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.7a + a2 = 0.1 The a term is -0.7a. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7a + 0.1225 + a2 = 0.1 + 0.1225 Reorder the terms: 0.1225 + -0.7a + a2 = 0.1 + 0.1225 Combine like terms: 0.1 + 0.1225 = 0.2225 0.1225 + -0.7a + a2 = 0.2225 Factor a perfect square on the left side: (a + -0.35)(a + -0.35) = 0.2225 Calculate the square root of the right side: 0.471699057 Break this problem into two subproblems by setting (a + -0.35) equal to 0.471699057 and -0.471699057.Subproblem 1
a + -0.35 = 0.471699057 Simplifying a + -0.35 = 0.471699057 Reorder the terms: -0.35 + a = 0.471699057 Solving -0.35 + a = 0.471699057 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + a = 0.471699057 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + a = 0.471699057 + 0.35 a = 0.471699057 + 0.35 Combine like terms: 0.471699057 + 0.35 = 0.821699057 a = 0.821699057 Simplifying a = 0.821699057Subproblem 2
a + -0.35 = -0.471699057 Simplifying a + -0.35 = -0.471699057 Reorder the terms: -0.35 + a = -0.471699057 Solving -0.35 + a = -0.471699057 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + a = -0.471699057 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + a = -0.471699057 + 0.35 a = -0.471699057 + 0.35 Combine like terms: -0.471699057 + 0.35 = -0.121699057 a = -0.121699057 Simplifying a = -0.121699057Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.821699057, -0.121699057}
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