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Simplifying -4.9x2 + 7.6x + 25 = 0 Reorder the terms: 25 + 7.6x + -4.9x2 = 0 Solving 25 + 7.6x + -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'. -5.102040816 + -1.551020408x + x2 = 0 Move the constant term to the right: Add '5.102040816' to each side of the equation. -5.102040816 + -1.551020408x + 5.102040816 + x2 = 0 + 5.102040816 Reorder the terms: -5.102040816 + 5.102040816 + -1.551020408x + x2 = 0 + 5.102040816 Combine like terms: -5.102040816 + 5.102040816 = 0.000000000 0.000000000 + -1.551020408x + x2 = 0 + 5.102040816 -1.551020408x + x2 = 0 + 5.102040816 Combine like terms: 0 + 5.102040816 = 5.102040816 -1.551020408x + x2 = 5.102040816 The x term is -1.551020408x. Take half its coefficient (-0.775510204). Square it (0.6014160765) and add it to both sides. Add '0.6014160765' to each side of the equation. -1.551020408x + 0.6014160765 + x2 = 5.102040816 + 0.6014160765 Reorder the terms: 0.6014160765 + -1.551020408x + x2 = 5.102040816 + 0.6014160765 Combine like terms: 5.102040816 + 0.6014160765 = 5.7034568925 0.6014160765 + -1.551020408x + x2 = 5.7034568925 Factor a perfect square on the left side: (x + -0.775510204)(x + -0.775510204) = 5.7034568925 Calculate the square root of the right side: 2.388191134 Break this problem into two subproblems by setting (x + -0.775510204) equal to 2.388191134 and -2.388191134.Subproblem 1
x + -0.775510204 = 2.388191134 Simplifying x + -0.775510204 = 2.388191134 Reorder the terms: -0.775510204 + x = 2.388191134 Solving -0.775510204 + x = 2.388191134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775510204' to each side of the equation. -0.775510204 + 0.775510204 + x = 2.388191134 + 0.775510204 Combine like terms: -0.775510204 + 0.775510204 = 0.000000000 0.000000000 + x = 2.388191134 + 0.775510204 x = 2.388191134 + 0.775510204 Combine like terms: 2.388191134 + 0.775510204 = 3.163701338 x = 3.163701338 Simplifying x = 3.163701338Subproblem 2
x + -0.775510204 = -2.388191134 Simplifying x + -0.775510204 = -2.388191134 Reorder the terms: -0.775510204 + x = -2.388191134 Solving -0.775510204 + x = -2.388191134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.775510204' to each side of the equation. -0.775510204 + 0.775510204 + x = -2.388191134 + 0.775510204 Combine like terms: -0.775510204 + 0.775510204 = 0.000000000 0.000000000 + x = -2.388191134 + 0.775510204 x = -2.388191134 + 0.775510204 Combine like terms: -2.388191134 + 0.775510204 = -1.61268093 x = -1.61268093 Simplifying x = -1.61268093Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.163701338, -1.61268093}
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