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Simplifying -66x2 + 3900x + -5240 = 0 Reorder the terms: -5240 + 3900x + -66x2 = 0 Solving -5240 + 3900x + -66x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2620 + 1950x + -33x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2620 + 1950x + -33x2)' equal to zero and attempt to solve: Simplifying -2620 + 1950x + -33x2 = 0 Solving -2620 + 1950x + -33x2 = 0 Begin completing the square. Divide all terms by -33 the coefficient of the squared term: Divide each side by '-33'. 79.39393939 + -59.09090909x + x2 = 0 Move the constant term to the right: Add '-79.39393939' to each side of the equation. 79.39393939 + -59.09090909x + -79.39393939 + x2 = 0 + -79.39393939 Reorder the terms: 79.39393939 + -79.39393939 + -59.09090909x + x2 = 0 + -79.39393939 Combine like terms: 79.39393939 + -79.39393939 = 0.00000000 0.00000000 + -59.09090909x + x2 = 0 + -79.39393939 -59.09090909x + x2 = 0 + -79.39393939 Combine like terms: 0 + -79.39393939 = -79.39393939 -59.09090909x + x2 = -79.39393939 The x term is -59.09090909x. Take half its coefficient (-29.54545455). Square it (872.9338846) and add it to both sides. Add '872.9338846' to each side of the equation. -59.09090909x + 872.9338846 + x2 = -79.39393939 + 872.9338846 Reorder the terms: 872.9338846 + -59.09090909x + x2 = -79.39393939 + 872.9338846 Combine like terms: -79.39393939 + 872.9338846 = 793.53994521 872.9338846 + -59.09090909x + x2 = 793.53994521 Factor a perfect square on the left side: (x + -29.54545455)(x + -29.54545455) = 793.53994521 Calculate the square root of the right side: 28.169841058 Break this problem into two subproblems by setting (x + -29.54545455) equal to 28.169841058 and -28.169841058.Subproblem 1
x + -29.54545455 = 28.169841058 Simplifying x + -29.54545455 = 28.169841058 Reorder the terms: -29.54545455 + x = 28.169841058 Solving -29.54545455 + x = 28.169841058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.54545455' to each side of the equation. -29.54545455 + 29.54545455 + x = 28.169841058 + 29.54545455 Combine like terms: -29.54545455 + 29.54545455 = 0.00000000 0.00000000 + x = 28.169841058 + 29.54545455 x = 28.169841058 + 29.54545455 Combine like terms: 28.169841058 + 29.54545455 = 57.715295608 x = 57.715295608 Simplifying x = 57.715295608Subproblem 2
x + -29.54545455 = -28.169841058 Simplifying x + -29.54545455 = -28.169841058 Reorder the terms: -29.54545455 + x = -28.169841058 Solving -29.54545455 + x = -28.169841058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.54545455' to each side of the equation. -29.54545455 + 29.54545455 + x = -28.169841058 + 29.54545455 Combine like terms: -29.54545455 + 29.54545455 = 0.00000000 0.00000000 + x = -28.169841058 + 29.54545455 x = -28.169841058 + 29.54545455 Combine like terms: -28.169841058 + 29.54545455 = 1.375613492 x = 1.375613492 Simplifying x = 1.375613492Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.715295608, 1.375613492}Solution
x = {57.715295608, 1.375613492}
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