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Simplifying 4.9x2 + -20x + -50 = 0 Reorder the terms: -50 + -20x + 4.9x2 = 0 Solving -50 + -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'. -10.20408163 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + -4.081632653x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + -4.081632653x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + -4.081632653x + x2 = 0 + 10.20408163 -4.081632653x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 -4.081632653x + x2 = 10.20408163 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 = 10.20408163 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = 10.20408163 + 4.164931281 Combine like terms: 10.20408163 + 4.164931281 = 14.369012911 4.164931281 + -4.081632653x + x2 = 14.369012911 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 14.369012911 Calculate the square root of the right side: 3.790648086 Break this problem into two subproblems by setting (x + -2.040816327) equal to 3.790648086 and -3.790648086.Subproblem 1
x + -2.040816327 = 3.790648086 Simplifying x + -2.040816327 = 3.790648086 Reorder the terms: -2.040816327 + x = 3.790648086 Solving -2.040816327 + x = 3.790648086 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 = 3.790648086 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 3.790648086 + 2.040816327 x = 3.790648086 + 2.040816327 Combine like terms: 3.790648086 + 2.040816327 = 5.831464413 x = 5.831464413 Simplifying x = 5.831464413Subproblem 2
x + -2.040816327 = -3.790648086 Simplifying x + -2.040816327 = -3.790648086 Reorder the terms: -2.040816327 + x = -3.790648086 Solving -2.040816327 + x = -3.790648086 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 = -3.790648086 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -3.790648086 + 2.040816327 x = -3.790648086 + 2.040816327 Combine like terms: -3.790648086 + 2.040816327 = -1.749831759 x = -1.749831759 Simplifying x = -1.749831759Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.831464413, -1.749831759}
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