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Simplifying 4x2 + -44x + 90 = 0 Reorder the terms: 90 + -44x + 4x2 = 0 Solving 90 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -22x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + -22x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + -22x + 2x2 = 0 Solving 45 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + -11x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -11x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -11x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -11x + x2 = 0 + -22.5 -11x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -11x + x2 = -22.5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -22.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -22.5 + 30.25 Combine like terms: -22.5 + 30.25 = 7.75 30.25 + -11x + x2 = 7.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + -5.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + -5.5 = 2.783882181 Simplifying x + -5.5 = 2.783882181 Reorder the terms: -5.5 + x = 2.783882181 Solving -5.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.783882181 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.783882181 + 5.5 x = 2.783882181 + 5.5 Combine like terms: 2.783882181 + 5.5 = 8.283882181 x = 8.283882181 Simplifying x = 8.283882181Subproblem 2
x + -5.5 = -2.783882181 Simplifying x + -5.5 = -2.783882181 Reorder the terms: -5.5 + x = -2.783882181 Solving -5.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.783882181 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.783882181 + 5.5 x = -2.783882181 + 5.5 Combine like terms: -2.783882181 + 5.5 = 2.716117819 x = 2.716117819 Simplifying x = 2.716117819Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.283882181, 2.716117819}Solution
x = {8.283882181, 2.716117819}
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