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Simplifying 4x2 + -44x + 100 = 0 Reorder the terms: 100 + -44x + 4x2 = 0 Solving 100 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -11x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -11x + x2)' equal to zero and attempt to solve: Simplifying 25 + -11x + x2 = 0 Solving 25 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -11x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -11x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -11x + x2 = 0 + -25 -11x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -11x + x2 = -25 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 = -25 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -25 + 30.25 Combine like terms: -25 + 30.25 = 5.25 30.25 + -11x + x2 = 5.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -5.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -5.5 = 2.291287847 Simplifying x + -5.5 = 2.291287847 Reorder the terms: -5.5 + x = 2.291287847 Solving -5.5 + x = 2.291287847 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 = 2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.291287847 + 5.5 x = 2.291287847 + 5.5 Combine like terms: 2.291287847 + 5.5 = 7.791287847 x = 7.791287847 Simplifying x = 7.791287847Subproblem 2
x + -5.5 = -2.291287847 Simplifying x + -5.5 = -2.291287847 Reorder the terms: -5.5 + x = -2.291287847 Solving -5.5 + x = -2.291287847 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 = -2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.291287847 + 5.5 x = -2.291287847 + 5.5 Combine like terms: -2.291287847 + 5.5 = 3.208712153 x = 3.208712153 Simplifying x = 3.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.791287847, 3.208712153}Solution
x = {7.791287847, 3.208712153}
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