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Simplifying 67x2 + 6x + 11 = 122 Reorder the terms: 11 + 6x + 67x2 = 122 Solving 11 + 6x + 67x2 = 122 Solving for variable 'x'. Reorder the terms: 11 + -122 + 6x + 67x2 = 122 + -122 Combine like terms: 11 + -122 = -111 -111 + 6x + 67x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -111 + 6x + 67x2 = 0 Begin completing the square. Divide all terms by 67 the coefficient of the squared term: Divide each side by '67'. -1.656716418 + 0.08955223881x + x2 = 0 Move the constant term to the right: Add '1.656716418' to each side of the equation. -1.656716418 + 0.08955223881x + 1.656716418 + x2 = 0 + 1.656716418 Reorder the terms: -1.656716418 + 1.656716418 + 0.08955223881x + x2 = 0 + 1.656716418 Combine like terms: -1.656716418 + 1.656716418 = 0.000000000 0.000000000 + 0.08955223881x + x2 = 0 + 1.656716418 0.08955223881x + x2 = 0 + 1.656716418 Combine like terms: 0 + 1.656716418 = 1.656716418 0.08955223881x + x2 = 1.656716418 The x term is 0.08955223881x. Take half its coefficient (0.04477611941). Square it (0.002004900869) and add it to both sides. Add '0.002004900869' to each side of the equation. 0.08955223881x + 0.002004900869 + x2 = 1.656716418 + 0.002004900869 Reorder the terms: 0.002004900869 + 0.08955223881x + x2 = 1.656716418 + 0.002004900869 Combine like terms: 1.656716418 + 0.002004900869 = 1.658721318869 0.002004900869 + 0.08955223881x + x2 = 1.658721318869 Factor a perfect square on the left side: (x + 0.04477611941)(x + 0.04477611941) = 1.658721318869 Calculate the square root of the right side: 1.287913553 Break this problem into two subproblems by setting (x + 0.04477611941) equal to 1.287913553 and -1.287913553.Subproblem 1
x + 0.04477611941 = 1.287913553 Simplifying x + 0.04477611941 = 1.287913553 Reorder the terms: 0.04477611941 + x = 1.287913553 Solving 0.04477611941 + x = 1.287913553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04477611941' to each side of the equation. 0.04477611941 + -0.04477611941 + x = 1.287913553 + -0.04477611941 Combine like terms: 0.04477611941 + -0.04477611941 = 0.00000000000 0.00000000000 + x = 1.287913553 + -0.04477611941 x = 1.287913553 + -0.04477611941 Combine like terms: 1.287913553 + -0.04477611941 = 1.24313743359 x = 1.24313743359 Simplifying x = 1.24313743359Subproblem 2
x + 0.04477611941 = -1.287913553 Simplifying x + 0.04477611941 = -1.287913553 Reorder the terms: 0.04477611941 + x = -1.287913553 Solving 0.04477611941 + x = -1.287913553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04477611941' to each side of the equation. 0.04477611941 + -0.04477611941 + x = -1.287913553 + -0.04477611941 Combine like terms: 0.04477611941 + -0.04477611941 = 0.00000000000 0.00000000000 + x = -1.287913553 + -0.04477611941 x = -1.287913553 + -0.04477611941 Combine like terms: -1.287913553 + -0.04477611941 = -1.33268967241 x = -1.33268967241 Simplifying x = -1.33268967241Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.24313743359, -1.33268967241}
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