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Simplifying -4.9x2 + 20x + 60 = 0 Reorder the terms: 60 + 20x + -4.9x2 = 0 Solving 60 + 20x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -12.24489796 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -4.081632653x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -4.081632653x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -4.081632653x + x2 = 0 + 12.24489796 -4.081632653x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -4.081632653x + x2 = 12.24489796 The x term is -4.081632653x. Take half its coefficient (-2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. -4.081632653x + 4.164931281 + x2 = 12.24489796 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 12.24489796 + 4.164931281 Combine like terms: 12.24489796 + 4.164931281 = 16.409829241 4.164931281 + -4.081632653x + x2 = 16.409829241 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 16.409829241 Calculate the square root of the right side: 4.050904744 Break this problem into two subproblems by setting (x + -2.040816327) equal to 4.050904744 and -4.050904744.Subproblem 1
x + -2.040816327 = 4.050904744 Simplifying x + -2.040816327 = 4.050904744 Reorder the terms: -2.040816327 + x = 4.050904744 Solving -2.040816327 + x = 4.050904744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = 4.050904744 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 4.050904744 + 2.040816327 x = 4.050904744 + 2.040816327 Combine like terms: 4.050904744 + 2.040816327 = 6.091721071 x = 6.091721071 Simplifying x = 6.091721071Subproblem 2
x + -2.040816327 = -4.050904744 Simplifying x + -2.040816327 = -4.050904744 Reorder the terms: -2.040816327 + x = -4.050904744 Solving -2.040816327 + x = -4.050904744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.040816327' to each side of the equation. -2.040816327 + 2.040816327 + x = -4.050904744 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -4.050904744 + 2.040816327 x = -4.050904744 + 2.040816327 Combine like terms: -4.050904744 + 2.040816327 = -2.010088417 x = -2.010088417 Simplifying x = -2.010088417Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.091721071, -2.010088417}
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