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Simplifying 4.9x2 + -20x + -40 = 0 Reorder the terms: -40 + -20x + 4.9x2 = 0 Solving -40 + -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'. -8.163265306 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -4.081632653x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -4.081632653x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -4.081632653x + x2 = 0 + 8.163265306 -4.081632653x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -4.081632653x + x2 = 8.163265306 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 = 8.163265306 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 8.163265306 + 4.164931281 Combine like terms: 8.163265306 + 4.164931281 = 12.328196587 4.164931281 + -4.081632653x + x2 = 12.328196587 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 12.328196587 Calculate the square root of the right side: 3.511153171 Break this problem into two subproblems by setting (x + -2.040816327) equal to 3.511153171 and -3.511153171.Subproblem 1
x + -2.040816327 = 3.511153171 Simplifying x + -2.040816327 = 3.511153171 Reorder the terms: -2.040816327 + x = 3.511153171 Solving -2.040816327 + x = 3.511153171 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 = 3.511153171 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 3.511153171 + 2.040816327 x = 3.511153171 + 2.040816327 Combine like terms: 3.511153171 + 2.040816327 = 5.551969498 x = 5.551969498 Simplifying x = 5.551969498Subproblem 2
x + -2.040816327 = -3.511153171 Simplifying x + -2.040816327 = -3.511153171 Reorder the terms: -2.040816327 + x = -3.511153171 Solving -2.040816327 + x = -3.511153171 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 = -3.511153171 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -3.511153171 + 2.040816327 x = -3.511153171 + 2.040816327 Combine like terms: -3.511153171 + 2.040816327 = -1.470336844 x = -1.470336844 Simplifying x = -1.470336844Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.551969498, -1.470336844}
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