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Simplifying -49x2 + -20x + -2 = 0 Reorder the terms: -2 + -20x + -49x2 = 0 Solving -2 + -20x + -49x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 20x + 49x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 20x + 49x2)' equal to zero and attempt to solve: Simplifying 2 + 20x + 49x2 = 0 Solving 2 + 20x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.04081632653 + 0.4081632653x + x2 = 0 Move the constant term to the right: Add '-0.04081632653' to each side of the equation. 0.04081632653 + 0.4081632653x + -0.04081632653 + x2 = 0 + -0.04081632653 Reorder the terms: 0.04081632653 + -0.04081632653 + 0.4081632653x + x2 = 0 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + 0.4081632653x + x2 = 0 + -0.04081632653 0.4081632653x + x2 = 0 + -0.04081632653 Combine like terms: 0 + -0.04081632653 = -0.04081632653 0.4081632653x + x2 = -0.04081632653 The x term is 0.4081632653x. Take half its coefficient (0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. 0.4081632653x + 0.04164931281 + x2 = -0.04081632653 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653x + x2 = -0.04081632653 + 0.04164931281 Combine like terms: -0.04081632653 + 0.04164931281 = 0.00083298628 0.04164931281 + 0.4081632653x + x2 = 0.00083298628 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 0.00083298628 Calculate the square root of the right side: 0.028861502 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 0.028861502 and -0.028861502.Subproblem 1
x + 0.2040816327 = 0.028861502 Simplifying x + 0.2040816327 = 0.028861502 Reorder the terms: 0.2040816327 + x = 0.028861502 Solving 0.2040816327 + x = 0.028861502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = 0.028861502 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 0.028861502 + -0.2040816327 x = 0.028861502 + -0.2040816327 Combine like terms: 0.028861502 + -0.2040816327 = -0.1752201307 x = -0.1752201307 Simplifying x = -0.1752201307Subproblem 2
x + 0.2040816327 = -0.028861502 Simplifying x + 0.2040816327 = -0.028861502 Reorder the terms: 0.2040816327 + x = -0.028861502 Solving 0.2040816327 + x = -0.028861502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = -0.028861502 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -0.028861502 + -0.2040816327 x = -0.028861502 + -0.2040816327 Combine like terms: -0.028861502 + -0.2040816327 = -0.2329431347 x = -0.2329431347 Simplifying x = -0.2329431347Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1752201307, -0.2329431347}Solution
x = {-0.1752201307, -0.2329431347}
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