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Simplifying 20x2 + -73x + -63 = 0 Reorder the terms: -63 + -73x + 20x2 = 0 Solving -63 + -73x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -3.15 + -3.65x + x2 = 0 Move the constant term to the right: Add '3.15' to each side of the equation. -3.15 + -3.65x + 3.15 + x2 = 0 + 3.15 Reorder the terms: -3.15 + 3.15 + -3.65x + x2 = 0 + 3.15 Combine like terms: -3.15 + 3.15 = 0.00 0.00 + -3.65x + x2 = 0 + 3.15 -3.65x + x2 = 0 + 3.15 Combine like terms: 0 + 3.15 = 3.15 -3.65x + x2 = 3.15 The x term is -3.65x. Take half its coefficient (-1.825). Square it (3.330625) and add it to both sides. Add '3.330625' to each side of the equation. -3.65x + 3.330625 + x2 = 3.15 + 3.330625 Reorder the terms: 3.330625 + -3.65x + x2 = 3.15 + 3.330625 Combine like terms: 3.15 + 3.330625 = 6.480625 3.330625 + -3.65x + x2 = 6.480625 Factor a perfect square on the left side: (x + -1.825)(x + -1.825) = 6.480625 Calculate the square root of the right side: 2.545707171 Break this problem into two subproblems by setting (x + -1.825) equal to 2.545707171 and -2.545707171.Subproblem 1
x + -1.825 = 2.545707171 Simplifying x + -1.825 = 2.545707171 Reorder the terms: -1.825 + x = 2.545707171 Solving -1.825 + x = 2.545707171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.825' to each side of the equation. -1.825 + 1.825 + x = 2.545707171 + 1.825 Combine like terms: -1.825 + 1.825 = 0.000 0.000 + x = 2.545707171 + 1.825 x = 2.545707171 + 1.825 Combine like terms: 2.545707171 + 1.825 = 4.370707171 x = 4.370707171 Simplifying x = 4.370707171Subproblem 2
x + -1.825 = -2.545707171 Simplifying x + -1.825 = -2.545707171 Reorder the terms: -1.825 + x = -2.545707171 Solving -1.825 + x = -2.545707171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.825' to each side of the equation. -1.825 + 1.825 + x = -2.545707171 + 1.825 Combine like terms: -1.825 + 1.825 = 0.000 0.000 + x = -2.545707171 + 1.825 x = -2.545707171 + 1.825 Combine like terms: -2.545707171 + 1.825 = -0.720707171 x = -0.720707171 Simplifying x = -0.720707171Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.370707171, -0.720707171}
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