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Simplifying 1.18x2 + -11.136x + 8 = 0 Reorder the terms: 8 + -11.136x + 1.18x2 = 0 Solving 8 + -11.136x + 1.18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.18 the coefficient of the squared term: Divide each side by '1.18'. 6.779661017 + -9.437288136x + x2 = 0 Move the constant term to the right: Add '-6.779661017' to each side of the equation. 6.779661017 + -9.437288136x + -6.779661017 + x2 = 0 + -6.779661017 Reorder the terms: 6.779661017 + -6.779661017 + -9.437288136x + x2 = 0 + -6.779661017 Combine like terms: 6.779661017 + -6.779661017 = 0.000000000 0.000000000 + -9.437288136x + x2 = 0 + -6.779661017 -9.437288136x + x2 = 0 + -6.779661017 Combine like terms: 0 + -6.779661017 = -6.779661017 -9.437288136x + x2 = -6.779661017 The x term is -9.437288136x. Take half its coefficient (-4.718644068). Square it (22.26560184) and add it to both sides. Add '22.26560184' to each side of the equation. -9.437288136x + 22.26560184 + x2 = -6.779661017 + 22.26560184 Reorder the terms: 22.26560184 + -9.437288136x + x2 = -6.779661017 + 22.26560184 Combine like terms: -6.779661017 + 22.26560184 = 15.485940823 22.26560184 + -9.437288136x + x2 = 15.485940823 Factor a perfect square on the left side: (x + -4.718644068)(x + -4.718644068) = 15.485940823 Calculate the square root of the right side: 3.935218015 Break this problem into two subproblems by setting (x + -4.718644068) equal to 3.935218015 and -3.935218015.Subproblem 1
x + -4.718644068 = 3.935218015 Simplifying x + -4.718644068 = 3.935218015 Reorder the terms: -4.718644068 + x = 3.935218015 Solving -4.718644068 + x = 3.935218015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.718644068' to each side of the equation. -4.718644068 + 4.718644068 + x = 3.935218015 + 4.718644068 Combine like terms: -4.718644068 + 4.718644068 = 0.000000000 0.000000000 + x = 3.935218015 + 4.718644068 x = 3.935218015 + 4.718644068 Combine like terms: 3.935218015 + 4.718644068 = 8.653862083 x = 8.653862083 Simplifying x = 8.653862083Subproblem 2
x + -4.718644068 = -3.935218015 Simplifying x + -4.718644068 = -3.935218015 Reorder the terms: -4.718644068 + x = -3.935218015 Solving -4.718644068 + x = -3.935218015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.718644068' to each side of the equation. -4.718644068 + 4.718644068 + x = -3.935218015 + 4.718644068 Combine like terms: -4.718644068 + 4.718644068 = 0.000000000 0.000000000 + x = -3.935218015 + 4.718644068 x = -3.935218015 + 4.718644068 Combine like terms: -3.935218015 + 4.718644068 = 0.783426053 x = 0.783426053 Simplifying x = 0.783426053Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.653862083, 0.783426053}
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