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Simplifying 98x2 + -73 + -105 = 4x Reorder the terms: -73 + -105 + 98x2 = 4x Combine like terms: -73 + -105 = -178 -178 + 98x2 = 4x Solving -178 + 98x2 = 4x Solving for variable 'x'. Reorder the terms: -178 + -4x + 98x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -178 + -4x + 98x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-89 + -2x + 49x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-89 + -2x + 49x2)' equal to zero and attempt to solve: Simplifying -89 + -2x + 49x2 = 0 Solving -89 + -2x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.816326531 + -0.04081632653x + x2 = 0 Move the constant term to the right: Add '1.816326531' to each side of the equation. -1.816326531 + -0.04081632653x + 1.816326531 + x2 = 0 + 1.816326531 Reorder the terms: -1.816326531 + 1.816326531 + -0.04081632653x + x2 = 0 + 1.816326531 Combine like terms: -1.816326531 + 1.816326531 = 0.000000000 0.000000000 + -0.04081632653x + x2 = 0 + 1.816326531 -0.04081632653x + x2 = 0 + 1.816326531 Combine like terms: 0 + 1.816326531 = 1.816326531 -0.04081632653x + x2 = 1.816326531 The x term is -0.04081632653x. Take half its coefficient (-0.02040816327). Square it (0.0004164931281) and add it to both sides. Add '0.0004164931281' to each side of the equation. -0.04081632653x + 0.0004164931281 + x2 = 1.816326531 + 0.0004164931281 Reorder the terms: 0.0004164931281 + -0.04081632653x + x2 = 1.816326531 + 0.0004164931281 Combine like terms: 1.816326531 + 0.0004164931281 = 1.8167430241281 0.0004164931281 + -0.04081632653x + x2 = 1.8167430241281 Factor a perfect square on the left side: (x + -0.02040816327)(x + -0.02040816327) = 1.8167430241281 Calculate the square root of the right side: 1.3478661 Break this problem into two subproblems by setting (x + -0.02040816327) equal to 1.3478661 and -1.3478661.Subproblem 1
x + -0.02040816327 = 1.3478661 Simplifying x + -0.02040816327 = 1.3478661 Reorder the terms: -0.02040816327 + x = 1.3478661 Solving -0.02040816327 + x = 1.3478661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02040816327' to each side of the equation. -0.02040816327 + 0.02040816327 + x = 1.3478661 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + x = 1.3478661 + 0.02040816327 x = 1.3478661 + 0.02040816327 Combine like terms: 1.3478661 + 0.02040816327 = 1.36827426327 x = 1.36827426327 Simplifying x = 1.36827426327Subproblem 2
x + -0.02040816327 = -1.3478661 Simplifying x + -0.02040816327 = -1.3478661 Reorder the terms: -0.02040816327 + x = -1.3478661 Solving -0.02040816327 + x = -1.3478661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02040816327' to each side of the equation. -0.02040816327 + 0.02040816327 + x = -1.3478661 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + x = -1.3478661 + 0.02040816327 x = -1.3478661 + 0.02040816327 Combine like terms: -1.3478661 + 0.02040816327 = -1.32745793673 x = -1.32745793673 Simplifying x = -1.32745793673Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.36827426327, -1.32745793673}Solution
x = {1.36827426327, -1.32745793673}
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