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Simplifying -9.8x2 + 40x + 60 = 0 Reorder the terms: 60 + 40x + -9.8x2 = 0 Solving 60 + 40x + -9.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -6.12244898 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -4.081632653x + 6.12244898 + x2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -4.081632653x + x2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -4.081632653x + x2 = 0 + 6.12244898 -4.081632653x + x2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -4.081632653x + x2 = 6.12244898 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 = 6.12244898 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 6.12244898 + 4.164931281 Combine like terms: 6.12244898 + 4.164931281 = 10.287380261 4.164931281 + -4.081632653x + x2 = 10.287380261 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 10.287380261 Calculate the square root of the right side: 3.207394622 Break this problem into two subproblems by setting (x + -2.040816327) equal to 3.207394622 and -3.207394622.Subproblem 1
x + -2.040816327 = 3.207394622 Simplifying x + -2.040816327 = 3.207394622 Reorder the terms: -2.040816327 + x = 3.207394622 Solving -2.040816327 + x = 3.207394622 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 = 3.207394622 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 3.207394622 + 2.040816327 x = 3.207394622 + 2.040816327 Combine like terms: 3.207394622 + 2.040816327 = 5.248210949 x = 5.248210949 Simplifying x = 5.248210949Subproblem 2
x + -2.040816327 = -3.207394622 Simplifying x + -2.040816327 = -3.207394622 Reorder the terms: -2.040816327 + x = -3.207394622 Solving -2.040816327 + x = -3.207394622 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 = -3.207394622 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -3.207394622 + 2.040816327 x = -3.207394622 + 2.040816327 Combine like terms: -3.207394622 + 2.040816327 = -1.166578295 x = -1.166578295 Simplifying x = -1.166578295Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.248210949, -1.166578295}
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