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Simplifying 6a * 6a + -5a = 99 Reorder the terms for easier multiplication: 6 * 6a * a + -5a = 99 Multiply 6 * 6 36a * a + -5a = 99 Multiply a * a 36a2 + -5a = 99 Reorder the terms: -5a + 36a2 = 99 Solving -5a + 36a2 = 99 Solving for variable 'a'. Reorder the terms: -99 + -5a + 36a2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -5a + 36a2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -2.75 + -0.1388888889a + a2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -0.1388888889a + 2.75 + a2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -0.1388888889a + a2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -0.1388888889a + a2 = 0 + 2.75 -0.1388888889a + a2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -0.1388888889a + a2 = 2.75 The a term is -0.1388888889a. Take half its coefficient (-0.06944444445). Square it (0.004822530865) and add it to both sides. Add '0.004822530865' to each side of the equation. -0.1388888889a + 0.004822530865 + a2 = 2.75 + 0.004822530865 Reorder the terms: 0.004822530865 + -0.1388888889a + a2 = 2.75 + 0.004822530865 Combine like terms: 2.75 + 0.004822530865 = 2.754822530865 0.004822530865 + -0.1388888889a + a2 = 2.754822530865 Factor a perfect square on the left side: (a + -0.06944444445)(a + -0.06944444445) = 2.754822530865 Calculate the square root of the right side: 1.659765806 Break this problem into two subproblems by setting (a + -0.06944444445) equal to 1.659765806 and -1.659765806.Subproblem 1
a + -0.06944444445 = 1.659765806 Simplifying a + -0.06944444445 = 1.659765806 Reorder the terms: -0.06944444445 + a = 1.659765806 Solving -0.06944444445 + a = 1.659765806 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + a = 1.659765806 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + a = 1.659765806 + 0.06944444445 a = 1.659765806 + 0.06944444445 Combine like terms: 1.659765806 + 0.06944444445 = 1.72921025045 a = 1.72921025045 Simplifying a = 1.72921025045Subproblem 2
a + -0.06944444445 = -1.659765806 Simplifying a + -0.06944444445 = -1.659765806 Reorder the terms: -0.06944444445 + a = -1.659765806 Solving -0.06944444445 + a = -1.659765806 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + a = -1.659765806 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + a = -1.659765806 + 0.06944444445 a = -1.659765806 + 0.06944444445 Combine like terms: -1.659765806 + 0.06944444445 = -1.59032136155 a = -1.59032136155 Simplifying a = -1.59032136155Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.72921025045, -1.59032136155}
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