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Simplifying -4.9x2 + 25x + 5 = 0 Reorder the terms: 5 + 25x + -4.9x2 = 0 Solving 5 + 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'. -1.020408163 + -5.102040816x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -5.102040816x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -5.102040816x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -5.102040816x + x2 = 0 + 1.020408163 -5.102040816x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -5.102040816x + x2 = 1.020408163 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 = 1.020408163 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816x + x2 = 1.020408163 + 6.507705122 Combine like terms: 1.020408163 + 6.507705122 = 7.528113285 6.507705122 + -5.102040816x + x2 = 7.528113285 Factor a perfect square on the left side: (x + -2.551020408)(x + -2.551020408) = 7.528113285 Calculate the square root of the right side: 2.743740747 Break this problem into two subproblems by setting (x + -2.551020408) equal to 2.743740747 and -2.743740747.Subproblem 1
x + -2.551020408 = 2.743740747 Simplifying x + -2.551020408 = 2.743740747 Reorder the terms: -2.551020408 + x = 2.743740747 Solving -2.551020408 + x = 2.743740747 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 = 2.743740747 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + x = 2.743740747 + 2.551020408 x = 2.743740747 + 2.551020408 Combine like terms: 2.743740747 + 2.551020408 = 5.294761155 x = 5.294761155 Simplifying x = 5.294761155Subproblem 2
x + -2.551020408 = -2.743740747 Simplifying x + -2.551020408 = -2.743740747 Reorder the terms: -2.551020408 + x = -2.743740747 Solving -2.551020408 + x = -2.743740747 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 = -2.743740747 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + x = -2.743740747 + 2.551020408 x = -2.743740747 + 2.551020408 Combine like terms: -2.743740747 + 2.551020408 = -0.192720339 x = -0.192720339 Simplifying x = -0.192720339Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.294761155, -0.192720339}
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