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Simplifying 26x2 + -63x + -4 = 0 Reorder the terms: -4 + -63x + 26x2 = 0 Solving -4 + -63x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.1538461538 + -2.423076923x + x2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -2.423076923x + 0.1538461538 + x2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -2.423076923x + x2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -2.423076923x + x2 = 0 + 0.1538461538 -2.423076923x + x2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -2.423076923x + x2 = 0.1538461538 The x term is -2.423076923x. Take half its coefficient (-1.211538462). Square it (1.467825445) and add it to both sides. Add '1.467825445' to each side of the equation. -2.423076923x + 1.467825445 + x2 = 0.1538461538 + 1.467825445 Reorder the terms: 1.467825445 + -2.423076923x + x2 = 0.1538461538 + 1.467825445 Combine like terms: 0.1538461538 + 1.467825445 = 1.6216715988 1.467825445 + -2.423076923x + x2 = 1.6216715988 Factor a perfect square on the left side: (x + -1.211538462)(x + -1.211538462) = 1.6216715988 Calculate the square root of the right side: 1.273448703 Break this problem into two subproblems by setting (x + -1.211538462) equal to 1.273448703 and -1.273448703.Subproblem 1
x + -1.211538462 = 1.273448703 Simplifying x + -1.211538462 = 1.273448703 Reorder the terms: -1.211538462 + x = 1.273448703 Solving -1.211538462 + x = 1.273448703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.211538462' to each side of the equation. -1.211538462 + 1.211538462 + x = 1.273448703 + 1.211538462 Combine like terms: -1.211538462 + 1.211538462 = 0.000000000 0.000000000 + x = 1.273448703 + 1.211538462 x = 1.273448703 + 1.211538462 Combine like terms: 1.273448703 + 1.211538462 = 2.484987165 x = 2.484987165 Simplifying x = 2.484987165Subproblem 2
x + -1.211538462 = -1.273448703 Simplifying x + -1.211538462 = -1.273448703 Reorder the terms: -1.211538462 + x = -1.273448703 Solving -1.211538462 + x = -1.273448703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.211538462' to each side of the equation. -1.211538462 + 1.211538462 + x = -1.273448703 + 1.211538462 Combine like terms: -1.211538462 + 1.211538462 = 0.000000000 0.000000000 + x = -1.273448703 + 1.211538462 x = -1.273448703 + 1.211538462 Combine like terms: -1.273448703 + 1.211538462 = -0.061910241 x = -0.061910241 Simplifying x = -0.061910241Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.484987165, -0.061910241}
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