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Simplifying a2 + -111a + -3510 = 0 Reorder the terms: -3510 + -111a + a2 = 0 Solving -3510 + -111a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '3510' to each side of the equation. -3510 + -111a + 3510 + a2 = 0 + 3510 Reorder the terms: -3510 + 3510 + -111a + a2 = 0 + 3510 Combine like terms: -3510 + 3510 = 0 0 + -111a + a2 = 0 + 3510 -111a + a2 = 0 + 3510 Combine like terms: 0 + 3510 = 3510 -111a + a2 = 3510 The a term is -111a. Take half its coefficient (-55.5). Square it (3080.25) and add it to both sides. Add '3080.25' to each side of the equation. -111a + 3080.25 + a2 = 3510 + 3080.25 Reorder the terms: 3080.25 + -111a + a2 = 3510 + 3080.25 Combine like terms: 3510 + 3080.25 = 6590.25 3080.25 + -111a + a2 = 6590.25 Factor a perfect square on the left side: (a + -55.5)(a + -55.5) = 6590.25 Calculate the square root of the right side: 81.180354766 Break this problem into two subproblems by setting (a + -55.5) equal to 81.180354766 and -81.180354766.Subproblem 1
a + -55.5 = 81.180354766 Simplifying a + -55.5 = 81.180354766 Reorder the terms: -55.5 + a = 81.180354766 Solving -55.5 + a = 81.180354766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '55.5' to each side of the equation. -55.5 + 55.5 + a = 81.180354766 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + a = 81.180354766 + 55.5 a = 81.180354766 + 55.5 Combine like terms: 81.180354766 + 55.5 = 136.680354766 a = 136.680354766 Simplifying a = 136.680354766Subproblem 2
a + -55.5 = -81.180354766 Simplifying a + -55.5 = -81.180354766 Reorder the terms: -55.5 + a = -81.180354766 Solving -55.5 + a = -81.180354766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '55.5' to each side of the equation. -55.5 + 55.5 + a = -81.180354766 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + a = -81.180354766 + 55.5 a = -81.180354766 + 55.5 Combine like terms: -81.180354766 + 55.5 = -25.680354766 a = -25.680354766 Simplifying a = -25.680354766Solution
The solution to the problem is based on the solutions from the subproblems. a = {136.680354766, -25.680354766}
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