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Simplifying 3.01x2 + 12.12x + -22.98 = 0 Reorder the terms: -22.98 + 12.12x + 3.01x2 = 0 Solving -22.98 + 12.12x + 3.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.01 the coefficient of the squared term: Divide each side by '3.01'. -7.634551495 + 4.026578073x + x2 = 0 Move the constant term to the right: Add '7.634551495' to each side of the equation. -7.634551495 + 4.026578073x + 7.634551495 + x2 = 0 + 7.634551495 Reorder the terms: -7.634551495 + 7.634551495 + 4.026578073x + x2 = 0 + 7.634551495 Combine like terms: -7.634551495 + 7.634551495 = 0.000000000 0.000000000 + 4.026578073x + x2 = 0 + 7.634551495 4.026578073x + x2 = 0 + 7.634551495 Combine like terms: 0 + 7.634551495 = 7.634551495 4.026578073x + x2 = 7.634551495 The x term is 4.026578073x. Take half its coefficient (2.013289037). Square it (4.053332747) and add it to both sides. Add '4.053332747' to each side of the equation. 4.026578073x + 4.053332747 + x2 = 7.634551495 + 4.053332747 Reorder the terms: 4.053332747 + 4.026578073x + x2 = 7.634551495 + 4.053332747 Combine like terms: 7.634551495 + 4.053332747 = 11.687884242 4.053332747 + 4.026578073x + x2 = 11.687884242 Factor a perfect square on the left side: (x + 2.013289037)(x + 2.013289037) = 11.687884242 Calculate the square root of the right side: 3.418754779 Break this problem into two subproblems by setting (x + 2.013289037) equal to 3.418754779 and -3.418754779.Subproblem 1
x + 2.013289037 = 3.418754779 Simplifying x + 2.013289037 = 3.418754779 Reorder the terms: 2.013289037 + x = 3.418754779 Solving 2.013289037 + x = 3.418754779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.013289037' to each side of the equation. 2.013289037 + -2.013289037 + x = 3.418754779 + -2.013289037 Combine like terms: 2.013289037 + -2.013289037 = 0.000000000 0.000000000 + x = 3.418754779 + -2.013289037 x = 3.418754779 + -2.013289037 Combine like terms: 3.418754779 + -2.013289037 = 1.405465742 x = 1.405465742 Simplifying x = 1.405465742Subproblem 2
x + 2.013289037 = -3.418754779 Simplifying x + 2.013289037 = -3.418754779 Reorder the terms: 2.013289037 + x = -3.418754779 Solving 2.013289037 + x = -3.418754779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.013289037' to each side of the equation. 2.013289037 + -2.013289037 + x = -3.418754779 + -2.013289037 Combine like terms: 2.013289037 + -2.013289037 = 0.000000000 0.000000000 + x = -3.418754779 + -2.013289037 x = -3.418754779 + -2.013289037 Combine like terms: -3.418754779 + -2.013289037 = -5.432043816 x = -5.432043816 Simplifying x = -5.432043816Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.405465742, -5.432043816}
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