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Simplifying 10x2 + -21x + -50 = 0 Reorder the terms: -50 + -21x + 10x2 = 0 Solving -50 + -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'. -5 + -2.1x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.1x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2.1x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.1x + x2 = 0 + 5 -2.1x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.1x + x2 = 5 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 = 5 + 1.1025 Reorder the terms: 1.1025 + -2.1x + x2 = 5 + 1.1025 Combine like terms: 5 + 1.1025 = 6.1025 1.1025 + -2.1x + x2 = 6.1025 Factor a perfect square on the left side: (x + -1.05)(x + -1.05) = 6.1025 Calculate the square root of the right side: 2.470323865 Break this problem into two subproblems by setting (x + -1.05) equal to 2.470323865 and -2.470323865.Subproblem 1
x + -1.05 = 2.470323865 Simplifying x + -1.05 = 2.470323865 Reorder the terms: -1.05 + x = 2.470323865 Solving -1.05 + x = 2.470323865 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 = 2.470323865 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 2.470323865 + 1.05 x = 2.470323865 + 1.05 Combine like terms: 2.470323865 + 1.05 = 3.520323865 x = 3.520323865 Simplifying x = 3.520323865Subproblem 2
x + -1.05 = -2.470323865 Simplifying x + -1.05 = -2.470323865 Reorder the terms: -1.05 + x = -2.470323865 Solving -1.05 + x = -2.470323865 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 = -2.470323865 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -2.470323865 + 1.05 x = -2.470323865 + 1.05 Combine like terms: -2.470323865 + 1.05 = -1.420323865 x = -1.420323865 Simplifying x = -1.420323865Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.520323865, -1.420323865}
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