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Simplifying 48x2 + -1537x + -3076 = 0 Reorder the terms: -3076 + -1537x + 48x2 = 0 Solving -3076 + -1537x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -64.08333333 + -32.02083333x + x2 = 0 Move the constant term to the right: Add '64.08333333' to each side of the equation. -64.08333333 + -32.02083333x + 64.08333333 + x2 = 0 + 64.08333333 Reorder the terms: -64.08333333 + 64.08333333 + -32.02083333x + x2 = 0 + 64.08333333 Combine like terms: -64.08333333 + 64.08333333 = 0.00000000 0.00000000 + -32.02083333x + x2 = 0 + 64.08333333 -32.02083333x + x2 = 0 + 64.08333333 Combine like terms: 0 + 64.08333333 = 64.08333333 -32.02083333x + x2 = 64.08333333 The x term is -32.02083333x. Take half its coefficient (-16.01041667). Square it (256.3334419) and add it to both sides. Add '256.3334419' to each side of the equation. -32.02083333x + 256.3334419 + x2 = 64.08333333 + 256.3334419 Reorder the terms: 256.3334419 + -32.02083333x + x2 = 64.08333333 + 256.3334419 Combine like terms: 64.08333333 + 256.3334419 = 320.41677523 256.3334419 + -32.02083333x + x2 = 320.41677523 Factor a perfect square on the left side: (x + -16.01041667)(x + -16.01041667) = 320.41677523 Calculate the square root of the right side: 17.900189251 Break this problem into two subproblems by setting (x + -16.01041667) equal to 17.900189251 and -17.900189251.Subproblem 1
x + -16.01041667 = 17.900189251 Simplifying x + -16.01041667 = 17.900189251 Reorder the terms: -16.01041667 + x = 17.900189251 Solving -16.01041667 + x = 17.900189251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.01041667' to each side of the equation. -16.01041667 + 16.01041667 + x = 17.900189251 + 16.01041667 Combine like terms: -16.01041667 + 16.01041667 = 0.00000000 0.00000000 + x = 17.900189251 + 16.01041667 x = 17.900189251 + 16.01041667 Combine like terms: 17.900189251 + 16.01041667 = 33.910605921 x = 33.910605921 Simplifying x = 33.910605921Subproblem 2
x + -16.01041667 = -17.900189251 Simplifying x + -16.01041667 = -17.900189251 Reorder the terms: -16.01041667 + x = -17.900189251 Solving -16.01041667 + x = -17.900189251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.01041667' to each side of the equation. -16.01041667 + 16.01041667 + x = -17.900189251 + 16.01041667 Combine like terms: -16.01041667 + 16.01041667 = 0.00000000 0.00000000 + x = -17.900189251 + 16.01041667 x = -17.900189251 + 16.01041667 Combine like terms: -17.900189251 + 16.01041667 = -1.889772581 x = -1.889772581 Simplifying x = -1.889772581Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.910605921, -1.889772581}
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