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Simplifying 4x2 = 22x + 24 Reorder the terms: 4x2 = 24 + 22x Solving 4x2 = 24 + 22x Solving for variable 'x'. Reorder the terms: -24 + -22x + 4x2 = 24 + 22x + -24 + -22x Reorder the terms: -24 + -22x + 4x2 = 24 + -24 + 22x + -22x Combine like terms: 24 + -24 = 0 -24 + -22x + 4x2 = 0 + 22x + -22x -24 + -22x + 4x2 = 22x + -22x Combine like terms: 22x + -22x = 0 -24 + -22x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying -12 + -11x + 2x2 = 0 Solving -12 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -5.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -5.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.5x + x2 = 0 + 6 -5.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.5x + x2 = 6 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 6 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + -5.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -2.75 = 3.682729966 Simplifying x + -2.75 = 3.682729966 Reorder the terms: -2.75 + x = 3.682729966 Solving -2.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.682729966 + 2.75 x = 3.682729966 + 2.75 Combine like terms: 3.682729966 + 2.75 = 6.432729966 x = 6.432729966 Simplifying x = 6.432729966Subproblem 2
x + -2.75 = -3.682729966 Simplifying x + -2.75 = -3.682729966 Reorder the terms: -2.75 + x = -3.682729966 Solving -2.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.682729966 + 2.75 x = -3.682729966 + 2.75 Combine like terms: -3.682729966 + 2.75 = -0.932729966 x = -0.932729966 Simplifying x = -0.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.432729966, -0.932729966}Solution
x = {6.432729966, -0.932729966}
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