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Simplifying 4x2 + -4x = 198 Reorder the terms: -4x + 4x2 = 198 Solving -4x + 4x2 = 198 Solving for variable 'x'. Reorder the terms: -198 + -4x + 4x2 = 198 + -198 Combine like terms: 198 + -198 = 0 -198 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-99 + -2x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-99 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -99 + -2x + 2x2 = 0 Solving -99 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -49.5 + -1x + x2 = 0 Move the constant term to the right: Add '49.5' to each side of the equation. -49.5 + -1x + 49.5 + x2 = 0 + 49.5 Reorder the terms: -49.5 + 49.5 + -1x + x2 = 0 + 49.5 Combine like terms: -49.5 + 49.5 = 0.0 0.0 + -1x + x2 = 0 + 49.5 -1x + x2 = 0 + 49.5 Combine like terms: 0 + 49.5 = 49.5 -1x + x2 = 49.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 49.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 49.5 + 0.25 Combine like terms: 49.5 + 0.25 = 49.75 0.25 + -1x + x2 = 49.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (x + -0.5) equal to 7.05336799 and -7.05336799.Subproblem 1
x + -0.5 = 7.05336799 Simplifying x + -0.5 = 7.05336799 Reorder the terms: -0.5 + x = 7.05336799 Solving -0.5 + x = 7.05336799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.05336799 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.05336799 + 0.5 x = 7.05336799 + 0.5 Combine like terms: 7.05336799 + 0.5 = 7.55336799 x = 7.55336799 Simplifying x = 7.55336799Subproblem 2
x + -0.5 = -7.05336799 Simplifying x + -0.5 = -7.05336799 Reorder the terms: -0.5 + x = -7.05336799 Solving -0.5 + x = -7.05336799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.05336799 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.05336799 + 0.5 x = -7.05336799 + 0.5 Combine like terms: -7.05336799 + 0.5 = -6.55336799 x = -6.55336799 Simplifying x = -6.55336799Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.55336799, -6.55336799}Solution
x = {7.55336799, -6.55336799}
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