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Simplifying 10x2 + -44x + 32 = 0 Reorder the terms: 32 + -44x + 10x2 = 0 Solving 32 + -44x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -22x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -22x + 5x2)' equal to zero and attempt to solve: Simplifying 16 + -22x + 5x2 = 0 Solving 16 + -22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -4.4x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -4.4x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -4.4x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -4.4x + x2 = 0 + -3.2 -4.4x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -4.4x + x2 = -3.2 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = -3.2 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = -3.2 + 4.84 Combine like terms: -3.2 + 4.84 = 1.64 4.84 + -4.4x + x2 = 1.64 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (x + -2.2) equal to 1.280624847 and -1.280624847.Subproblem 1
x + -2.2 = 1.280624847 Simplifying x + -2.2 = 1.280624847 Reorder the terms: -2.2 + x = 1.280624847 Solving -2.2 + x = 1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 1.280624847 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 1.280624847 + 2.2 x = 1.280624847 + 2.2 Combine like terms: 1.280624847 + 2.2 = 3.480624847 x = 3.480624847 Simplifying x = 3.480624847Subproblem 2
x + -2.2 = -1.280624847 Simplifying x + -2.2 = -1.280624847 Reorder the terms: -2.2 + x = -1.280624847 Solving -2.2 + x = -1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -1.280624847 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -1.280624847 + 2.2 x = -1.280624847 + 2.2 Combine like terms: -1.280624847 + 2.2 = 0.919375153 x = 0.919375153 Simplifying x = 0.919375153Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.480624847, 0.919375153}Solution
x = {3.480624847, 0.919375153}
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