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Simplifying 2.51x2 + -11.30x + -6.28 = 0 Reorder the terms: -6.28 + -11.30x + 2.51x2 = 0 Solving -6.28 + -11.30x + 2.51x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.51 the coefficient of the squared term: Divide each side by '2.51'. -2.501992032 + -4.501992032x + x2 = 0 Move the constant term to the right: Add '2.501992032' to each side of the equation. -2.501992032 + -4.501992032x + 2.501992032 + x2 = 0 + 2.501992032 Reorder the terms: -2.501992032 + 2.501992032 + -4.501992032x + x2 = 0 + 2.501992032 Combine like terms: -2.501992032 + 2.501992032 = 0.000000000 0.000000000 + -4.501992032x + x2 = 0 + 2.501992032 -4.501992032x + x2 = 0 + 2.501992032 Combine like terms: 0 + 2.501992032 = 2.501992032 -4.501992032x + x2 = 2.501992032 The x term is -4.501992032x. Take half its coefficient (-2.250996016). Square it (5.066983064) and add it to both sides. Add '5.066983064' to each side of the equation. -4.501992032x + 5.066983064 + x2 = 2.501992032 + 5.066983064 Reorder the terms: 5.066983064 + -4.501992032x + x2 = 2.501992032 + 5.066983064 Combine like terms: 2.501992032 + 5.066983064 = 7.568975096 5.066983064 + -4.501992032x + x2 = 7.568975096 Factor a perfect square on the left side: (x + -2.250996016)(x + -2.250996016) = 7.568975096 Calculate the square root of the right side: 2.751177038 Break this problem into two subproblems by setting (x + -2.250996016) equal to 2.751177038 and -2.751177038.Subproblem 1
x + -2.250996016 = 2.751177038 Simplifying x + -2.250996016 = 2.751177038 Reorder the terms: -2.250996016 + x = 2.751177038 Solving -2.250996016 + x = 2.751177038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.250996016' to each side of the equation. -2.250996016 + 2.250996016 + x = 2.751177038 + 2.250996016 Combine like terms: -2.250996016 + 2.250996016 = 0.000000000 0.000000000 + x = 2.751177038 + 2.250996016 x = 2.751177038 + 2.250996016 Combine like terms: 2.751177038 + 2.250996016 = 5.002173054 x = 5.002173054 Simplifying x = 5.002173054Subproblem 2
x + -2.250996016 = -2.751177038 Simplifying x + -2.250996016 = -2.751177038 Reorder the terms: -2.250996016 + x = -2.751177038 Solving -2.250996016 + x = -2.751177038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.250996016' to each side of the equation. -2.250996016 + 2.250996016 + x = -2.751177038 + 2.250996016 Combine like terms: -2.250996016 + 2.250996016 = 0.000000000 0.000000000 + x = -2.751177038 + 2.250996016 x = -2.751177038 + 2.250996016 Combine like terms: -2.751177038 + 2.250996016 = -0.500181022 x = -0.500181022 Simplifying x = -0.500181022Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.002173054, -0.500181022}
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