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Simplifying 4x2 + -44x + 110 = 0 Reorder the terms: 110 + -44x + 4x2 = 0 Solving 110 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -22x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -22x + 2x2)' equal to zero and attempt to solve: Simplifying 55 + -22x + 2x2 = 0 Solving 55 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27.5 + -11x + x2 = 0 Move the constant term to the right: Add '-27.5' to each side of the equation. 27.5 + -11x + -27.5 + x2 = 0 + -27.5 Reorder the terms: 27.5 + -27.5 + -11x + x2 = 0 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + -11x + x2 = 0 + -27.5 -11x + x2 = 0 + -27.5 Combine like terms: 0 + -27.5 = -27.5 -11x + x2 = -27.5 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 = -27.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -27.5 + 30.25 Combine like terms: -27.5 + 30.25 = 2.75 30.25 + -11x + x2 = 2.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -5.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -5.5 = 1.658312395 Simplifying x + -5.5 = 1.658312395 Reorder the terms: -5.5 + x = 1.658312395 Solving -5.5 + x = 1.658312395 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 = 1.658312395 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 1.658312395 + 5.5 x = 1.658312395 + 5.5 Combine like terms: 1.658312395 + 5.5 = 7.158312395 x = 7.158312395 Simplifying x = 7.158312395Subproblem 2
x + -5.5 = -1.658312395 Simplifying x + -5.5 = -1.658312395 Reorder the terms: -5.5 + x = -1.658312395 Solving -5.5 + x = -1.658312395 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 = -1.658312395 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -1.658312395 + 5.5 x = -1.658312395 + 5.5 Combine like terms: -1.658312395 + 5.5 = 3.841687605 x = 3.841687605 Simplifying x = 3.841687605Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.158312395, 3.841687605}Solution
x = {7.158312395, 3.841687605}
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