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Simplifying 4x2 + -116x + 198 = 0 Reorder the terms: 198 + -116x + 4x2 = 0 Solving 198 + -116x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(99 + -58x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(99 + -58x + 2x2)' equal to zero and attempt to solve: Simplifying 99 + -58x + 2x2 = 0 Solving 99 + -58x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 49.5 + -29x + x2 = 0 Move the constant term to the right: Add '-49.5' to each side of the equation. 49.5 + -29x + -49.5 + x2 = 0 + -49.5 Reorder the terms: 49.5 + -49.5 + -29x + x2 = 0 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + -29x + x2 = 0 + -49.5 -29x + x2 = 0 + -49.5 Combine like terms: 0 + -49.5 = -49.5 -29x + x2 = -49.5 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -49.5 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -49.5 + 210.25 Combine like terms: -49.5 + 210.25 = 160.75 210.25 + -29x + x2 = 160.75 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 160.75 Calculate the square root of the right side: 12.678722333 Break this problem into two subproblems by setting (x + -14.5) equal to 12.678722333 and -12.678722333.Subproblem 1
x + -14.5 = 12.678722333 Simplifying x + -14.5 = 12.678722333 Reorder the terms: -14.5 + x = 12.678722333 Solving -14.5 + x = 12.678722333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 12.678722333 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 12.678722333 + 14.5 x = 12.678722333 + 14.5 Combine like terms: 12.678722333 + 14.5 = 27.178722333 x = 27.178722333 Simplifying x = 27.178722333Subproblem 2
x + -14.5 = -12.678722333 Simplifying x + -14.5 = -12.678722333 Reorder the terms: -14.5 + x = -12.678722333 Solving -14.5 + x = -12.678722333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -12.678722333 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -12.678722333 + 14.5 x = -12.678722333 + 14.5 Combine like terms: -12.678722333 + 14.5 = 1.821277667 x = 1.821277667 Simplifying x = 1.821277667Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.178722333, 1.821277667}Solution
x = {27.178722333, 1.821277667}
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