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Simplifying 4.9x2 + -12x + 3.81 = 0 Reorder the terms: 3.81 + -12x + 4.9x2 = 0 Solving 3.81 + -12x + 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'. 0.7775510204 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '-0.7775510204' to each side of the equation. 0.7775510204 + -2.448979592x + -0.7775510204 + x2 = 0 + -0.7775510204 Reorder the terms: 0.7775510204 + -0.7775510204 + -2.448979592x + x2 = 0 + -0.7775510204 Combine like terms: 0.7775510204 + -0.7775510204 = 0.0000000000 0.0000000000 + -2.448979592x + x2 = 0 + -0.7775510204 -2.448979592x + x2 = 0 + -0.7775510204 Combine like terms: 0 + -0.7775510204 = -0.7775510204 -2.448979592x + x2 = -0.7775510204 The x term is -2.448979592x. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592x + 1.499375261 + x2 = -0.7775510204 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = -0.7775510204 + 1.499375261 Combine like terms: -0.7775510204 + 1.499375261 = 0.7218242406 1.499375261 + -2.448979592x + x2 = 0.7218242406 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 0.7218242406 Calculate the square root of the right side: 0.849602401 Break this problem into two subproblems by setting (x + -1.224489796) equal to 0.849602401 and -0.849602401.Subproblem 1
x + -1.224489796 = 0.849602401 Simplifying x + -1.224489796 = 0.849602401 Reorder the terms: -1.224489796 + x = 0.849602401 Solving -1.224489796 + x = 0.849602401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 0.849602401 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 0.849602401 + 1.224489796 x = 0.849602401 + 1.224489796 Combine like terms: 0.849602401 + 1.224489796 = 2.074092197 x = 2.074092197 Simplifying x = 2.074092197Subproblem 2
x + -1.224489796 = -0.849602401 Simplifying x + -1.224489796 = -0.849602401 Reorder the terms: -1.224489796 + x = -0.849602401 Solving -1.224489796 + x = -0.849602401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -0.849602401 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -0.849602401 + 1.224489796 x = -0.849602401 + 1.224489796 Combine like terms: -0.849602401 + 1.224489796 = 0.374887395 x = 0.374887395 Simplifying x = 0.374887395Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.074092197, 0.374887395}
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