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Simplifying 4x2 + 100x + 294 = 0 Reorder the terms: 294 + 100x + 4x2 = 0 Solving 294 + 100x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(147 + 50x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(147 + 50x + 2x2)' equal to zero and attempt to solve: Simplifying 147 + 50x + 2x2 = 0 Solving 147 + 50x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 73.5 + 25x + x2 = 0 Move the constant term to the right: Add '-73.5' to each side of the equation. 73.5 + 25x + -73.5 + x2 = 0 + -73.5 Reorder the terms: 73.5 + -73.5 + 25x + x2 = 0 + -73.5 Combine like terms: 73.5 + -73.5 = 0.0 0.0 + 25x + x2 = 0 + -73.5 25x + x2 = 0 + -73.5 Combine like terms: 0 + -73.5 = -73.5 25x + x2 = -73.5 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -73.5 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -73.5 + 156.25 Combine like terms: -73.5 + 156.25 = 82.75 156.25 + 25x + x2 = 82.75 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 82.75 Calculate the square root of the right side: 9.096702699 Break this problem into two subproblems by setting (x + 12.5) equal to 9.096702699 and -9.096702699.Subproblem 1
x + 12.5 = 9.096702699 Simplifying x + 12.5 = 9.096702699 Reorder the terms: 12.5 + x = 9.096702699 Solving 12.5 + x = 9.096702699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 9.096702699 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 9.096702699 + -12.5 x = 9.096702699 + -12.5 Combine like terms: 9.096702699 + -12.5 = -3.403297301 x = -3.403297301 Simplifying x = -3.403297301Subproblem 2
x + 12.5 = -9.096702699 Simplifying x + 12.5 = -9.096702699 Reorder the terms: 12.5 + x = -9.096702699 Solving 12.5 + x = -9.096702699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -9.096702699 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -9.096702699 + -12.5 x = -9.096702699 + -12.5 Combine like terms: -9.096702699 + -12.5 = -21.596702699 x = -21.596702699 Simplifying x = -21.596702699Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.403297301, -21.596702699}Solution
x = {-3.403297301, -21.596702699}
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