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Simplifying 10x2 + -21x + -21 = 0 Reorder the terms: -21 + -21x + 10x2 = 0 Solving -21 + -21x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + -2.1x + x2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -2.1x + 2.1 + x2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + -2.1x + x2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -2.1x + x2 = 0 + 2.1 -2.1x + x2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 -2.1x + x2 = 2.1 The x term is -2.1x. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1x + 1.1025 + x2 = 2.1 + 1.1025 Reorder the terms: 1.1025 + -2.1x + x2 = 2.1 + 1.1025 Combine like terms: 2.1 + 1.1025 = 3.2025 1.1025 + -2.1x + x2 = 3.2025 Factor a perfect square on the left side: (x + -1.05)(x + -1.05) = 3.2025 Calculate the square root of the right side: 1.789553017 Break this problem into two subproblems by setting (x + -1.05) equal to 1.789553017 and -1.789553017.Subproblem 1
x + -1.05 = 1.789553017 Simplifying x + -1.05 = 1.789553017 Reorder the terms: -1.05 + x = 1.789553017 Solving -1.05 + x = 1.789553017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 1.789553017 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 1.789553017 + 1.05 x = 1.789553017 + 1.05 Combine like terms: 1.789553017 + 1.05 = 2.839553017 x = 2.839553017 Simplifying x = 2.839553017Subproblem 2
x + -1.05 = -1.789553017 Simplifying x + -1.05 = -1.789553017 Reorder the terms: -1.05 + x = -1.789553017 Solving -1.05 + x = -1.789553017 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -1.789553017 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -1.789553017 + 1.05 x = -1.789553017 + 1.05 Combine like terms: -1.789553017 + 1.05 = -0.739553017 x = -0.739553017 Simplifying x = -0.739553017Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.839553017, -0.739553017}
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