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Simplifying 12.716x2 + -17.204x + -9.681 = 0 Reorder the terms: -9.681 + -17.204x + 12.716x2 = 0 Solving -9.681 + -17.204x + 12.716x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12.716 the coefficient of the squared term: Divide each side by '12.716'. -0.7613243158 + -1.352941176x + x2 = 0 Move the constant term to the right: Add '0.7613243158' to each side of the equation. -0.7613243158 + -1.352941176x + 0.7613243158 + x2 = 0 + 0.7613243158 Reorder the terms: -0.7613243158 + 0.7613243158 + -1.352941176x + x2 = 0 + 0.7613243158 Combine like terms: -0.7613243158 + 0.7613243158 = 0.0000000000 0.0000000000 + -1.352941176x + x2 = 0 + 0.7613243158 -1.352941176x + x2 = 0 + 0.7613243158 Combine like terms: 0 + 0.7613243158 = 0.7613243158 -1.352941176x + x2 = 0.7613243158 The x term is -1.352941176x. Take half its coefficient (-0.676470588). Square it (0.4576124564) and add it to both sides. Add '0.4576124564' to each side of the equation. -1.352941176x + 0.4576124564 + x2 = 0.7613243158 + 0.4576124564 Reorder the terms: 0.4576124564 + -1.352941176x + x2 = 0.7613243158 + 0.4576124564 Combine like terms: 0.7613243158 + 0.4576124564 = 1.2189367722 0.4576124564 + -1.352941176x + x2 = 1.2189367722 Factor a perfect square on the left side: (x + -0.676470588)(x + -0.676470588) = 1.2189367722 Calculate the square root of the right side: 1.104054696 Break this problem into two subproblems by setting (x + -0.676470588) equal to 1.104054696 and -1.104054696.Subproblem 1
x + -0.676470588 = 1.104054696 Simplifying x + -0.676470588 = 1.104054696 Reorder the terms: -0.676470588 + x = 1.104054696 Solving -0.676470588 + x = 1.104054696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.676470588' to each side of the equation. -0.676470588 + 0.676470588 + x = 1.104054696 + 0.676470588 Combine like terms: -0.676470588 + 0.676470588 = 0.000000000 0.000000000 + x = 1.104054696 + 0.676470588 x = 1.104054696 + 0.676470588 Combine like terms: 1.104054696 + 0.676470588 = 1.780525284 x = 1.780525284 Simplifying x = 1.780525284Subproblem 2
x + -0.676470588 = -1.104054696 Simplifying x + -0.676470588 = -1.104054696 Reorder the terms: -0.676470588 + x = -1.104054696 Solving -0.676470588 + x = -1.104054696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.676470588' to each side of the equation. -0.676470588 + 0.676470588 + x = -1.104054696 + 0.676470588 Combine like terms: -0.676470588 + 0.676470588 = 0.000000000 0.000000000 + x = -1.104054696 + 0.676470588 x = -1.104054696 + 0.676470588 Combine like terms: -1.104054696 + 0.676470588 = -0.427584108 x = -0.427584108 Simplifying x = -0.427584108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.780525284, -0.427584108}
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