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Simplifying 4.9x2 + 25x + -20 = 0 Reorder the terms: -20 + 25x + 4.9x2 = 0 Solving -20 + 25x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.081632653 + 5.102040816x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 5.102040816x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 5.102040816x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 5.102040816x + x2 = 0 + 4.081632653 5.102040816x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 5.102040816x + x2 = 4.081632653 The x term is 5.102040816x. Take half its coefficient (2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. 5.102040816x + 6.507705122 + x2 = 4.081632653 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816x + x2 = 4.081632653 + 6.507705122 Combine like terms: 4.081632653 + 6.507705122 = 10.589337775 6.507705122 + 5.102040816x + x2 = 10.589337775 Factor a perfect square on the left side: (x + 2.551020408)(x + 2.551020408) = 10.589337775 Calculate the square root of the right side: 3.254126269 Break this problem into two subproblems by setting (x + 2.551020408) equal to 3.254126269 and -3.254126269.Subproblem 1
x + 2.551020408 = 3.254126269 Simplifying x + 2.551020408 = 3.254126269 Reorder the terms: 2.551020408 + x = 3.254126269 Solving 2.551020408 + x = 3.254126269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + x = 3.254126269 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + x = 3.254126269 + -2.551020408 x = 3.254126269 + -2.551020408 Combine like terms: 3.254126269 + -2.551020408 = 0.703105861 x = 0.703105861 Simplifying x = 0.703105861Subproblem 2
x + 2.551020408 = -3.254126269 Simplifying x + 2.551020408 = -3.254126269 Reorder the terms: 2.551020408 + x = -3.254126269 Solving 2.551020408 + x = -3.254126269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + x = -3.254126269 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + x = -3.254126269 + -2.551020408 x = -3.254126269 + -2.551020408 Combine like terms: -3.254126269 + -2.551020408 = -5.805146677 x = -5.805146677 Simplifying x = -5.805146677Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.703105861, -5.805146677}
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