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Simplifying 0.142190879x2 + -0.390768708x + 0.002577829 = 0 Reorder the terms: 0.002577829 + -0.390768708x + 0.142190879x2 = 0 Solving 0.002577829 + -0.390768708x + 0.142190879x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.142190879 the coefficient of the squared term: Divide each side by '0.142190879'. 0.01812935554 + -2.748198132x + x2 = 0 Move the constant term to the right: Add '-0.01812935554' to each side of the equation. 0.01812935554 + -2.748198132x + -0.01812935554 + x2 = 0 + -0.01812935554 Reorder the terms: 0.01812935554 + -0.01812935554 + -2.748198132x + x2 = 0 + -0.01812935554 Combine like terms: 0.01812935554 + -0.01812935554 = 0.00000000000 0.00000000000 + -2.748198132x + x2 = 0 + -0.01812935554 -2.748198132x + x2 = 0 + -0.01812935554 Combine like terms: 0 + -0.01812935554 = -0.01812935554 -2.748198132x + x2 = -0.01812935554 The x term is -2.748198132x. Take half its coefficient (-1.374099066). Square it (1.888148243) and add it to both sides. Add '1.888148243' to each side of the equation. -2.748198132x + 1.888148243 + x2 = -0.01812935554 + 1.888148243 Reorder the terms: 1.888148243 + -2.748198132x + x2 = -0.01812935554 + 1.888148243 Combine like terms: -0.01812935554 + 1.888148243 = 1.87001888746 1.888148243 + -2.748198132x + x2 = 1.87001888746 Factor a perfect square on the left side: (x + -1.374099066)(x + -1.374099066) = 1.87001888746 Calculate the square root of the right side: 1.367486339 Break this problem into two subproblems by setting (x + -1.374099066) equal to 1.367486339 and -1.367486339.Subproblem 1
x + -1.374099066 = 1.367486339 Simplifying x + -1.374099066 = 1.367486339 Reorder the terms: -1.374099066 + x = 1.367486339 Solving -1.374099066 + x = 1.367486339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.374099066' to each side of the equation. -1.374099066 + 1.374099066 + x = 1.367486339 + 1.374099066 Combine like terms: -1.374099066 + 1.374099066 = 0.000000000 0.000000000 + x = 1.367486339 + 1.374099066 x = 1.367486339 + 1.374099066 Combine like terms: 1.367486339 + 1.374099066 = 2.741585405 x = 2.741585405 Simplifying x = 2.741585405Subproblem 2
x + -1.374099066 = -1.367486339 Simplifying x + -1.374099066 = -1.367486339 Reorder the terms: -1.374099066 + x = -1.367486339 Solving -1.374099066 + x = -1.367486339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.374099066' to each side of the equation. -1.374099066 + 1.374099066 + x = -1.367486339 + 1.374099066 Combine like terms: -1.374099066 + 1.374099066 = 0.000000000 0.000000000 + x = -1.367486339 + 1.374099066 x = -1.367486339 + 1.374099066 Combine like terms: -1.367486339 + 1.374099066 = 0.006612727 x = 0.006612727 Simplifying x = 0.006612727Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.741585405, 0.006612727}
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