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Simplifying 13x2 + 12x + 1 = 0 Reorder the terms: 1 + 12x + 13x2 = 0 Solving 1 + 12x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.07692307692 + 0.9230769231x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + 0.9230769231x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + 0.9230769231x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + 0.9230769231x + x2 = 0 + -0.07692307692 0.9230769231x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 0.9230769231x + x2 = -0.07692307692 The x term is 0.9230769231x. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231x + 0.2130177515 + x2 = -0.07692307692 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231x + x2 = -0.07692307692 + 0.2130177515 Combine like terms: -0.07692307692 + 0.2130177515 = 0.13609467458 0.2130177515 + 0.9230769231x + x2 = 0.13609467458 Factor a perfect square on the left side: (x + 0.4615384616)(x + 0.4615384616) = 0.13609467458 Calculate the square root of the right side: 0.368910117 Break this problem into two subproblems by setting (x + 0.4615384616) equal to 0.368910117 and -0.368910117.Subproblem 1
x + 0.4615384616 = 0.368910117 Simplifying x + 0.4615384616 = 0.368910117 Reorder the terms: 0.4615384616 + x = 0.368910117 Solving 0.4615384616 + x = 0.368910117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = 0.368910117 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = 0.368910117 + -0.4615384616 x = 0.368910117 + -0.4615384616 Combine like terms: 0.368910117 + -0.4615384616 = -0.0926283446 x = -0.0926283446 Simplifying x = -0.0926283446Subproblem 2
x + 0.4615384616 = -0.368910117 Simplifying x + 0.4615384616 = -0.368910117 Reorder the terms: 0.4615384616 + x = -0.368910117 Solving 0.4615384616 + x = -0.368910117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = -0.368910117 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = -0.368910117 + -0.4615384616 x = -0.368910117 + -0.4615384616 Combine like terms: -0.368910117 + -0.4615384616 = -0.8304485786 x = -0.8304485786 Simplifying x = -0.8304485786Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0926283446, -0.8304485786}
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