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Simplifying -4x2 + -110x + 294 = 0 Reorder the terms: 294 + -110x + -4x2 = 0 Solving 294 + -110x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(147 + -55x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(147 + -55x + -2x2)' equal to zero and attempt to solve: Simplifying 147 + -55x + -2x2 = 0 Solving 147 + -55x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -73.5 + 27.5x + x2 = 0 Move the constant term to the right: Add '73.5' to each side of the equation. -73.5 + 27.5x + 73.5 + x2 = 0 + 73.5 Reorder the terms: -73.5 + 73.5 + 27.5x + x2 = 0 + 73.5 Combine like terms: -73.5 + 73.5 = 0.0 0.0 + 27.5x + x2 = 0 + 73.5 27.5x + x2 = 0 + 73.5 Combine like terms: 0 + 73.5 = 73.5 27.5x + x2 = 73.5 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = 73.5 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = 73.5 + 189.0625 Combine like terms: 73.5 + 189.0625 = 262.5625 189.0625 + 27.5x + x2 = 262.5625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 262.5625 Calculate the square root of the right side: 16.203780423 Break this problem into two subproblems by setting (x + 13.75) equal to 16.203780423 and -16.203780423.Subproblem 1
x + 13.75 = 16.203780423 Simplifying x + 13.75 = 16.203780423 Reorder the terms: 13.75 + x = 16.203780423 Solving 13.75 + x = 16.203780423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 16.203780423 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 16.203780423 + -13.75 x = 16.203780423 + -13.75 Combine like terms: 16.203780423 + -13.75 = 2.453780423 x = 2.453780423 Simplifying x = 2.453780423Subproblem 2
x + 13.75 = -16.203780423 Simplifying x + 13.75 = -16.203780423 Reorder the terms: 13.75 + x = -16.203780423 Solving 13.75 + x = -16.203780423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -16.203780423 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -16.203780423 + -13.75 x = -16.203780423 + -13.75 Combine like terms: -16.203780423 + -13.75 = -29.953780423 x = -29.953780423 Simplifying x = -29.953780423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.453780423, -29.953780423}Solution
x = {2.453780423, -29.953780423}
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