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Simplifying 4x2 + -80x + 224 = 0 Reorder the terms: 224 + -80x + 4x2 = 0 Solving 224 + -80x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(56 + -20x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(56 + -20x + x2)' equal to zero and attempt to solve: Simplifying 56 + -20x + x2 = 0 Solving 56 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -20x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -20x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -20x + x2 = 0 + -56 -20x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -20x + x2 = -56 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -56 + 100 Reorder the terms: 100 + -20x + x2 = -56 + 100 Combine like terms: -56 + 100 = 44 100 + -20x + x2 = 44 Factor a perfect square on the left side: (x + -10)(x + -10) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + -10) equal to 6.633249581 and -6.633249581.Subproblem 1
x + -10 = 6.633249581 Simplifying x + -10 = 6.633249581 Reorder the terms: -10 + x = 6.633249581 Solving -10 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 6.633249581 + 10 Combine like terms: -10 + 10 = 0 0 + x = 6.633249581 + 10 x = 6.633249581 + 10 Combine like terms: 6.633249581 + 10 = 16.633249581 x = 16.633249581 Simplifying x = 16.633249581Subproblem 2
x + -10 = -6.633249581 Simplifying x + -10 = -6.633249581 Reorder the terms: -10 + x = -6.633249581 Solving -10 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -6.633249581 + 10 Combine like terms: -10 + 10 = 0 0 + x = -6.633249581 + 10 x = -6.633249581 + 10 Combine like terms: -6.633249581 + 10 = 3.366750419 x = 3.366750419 Simplifying x = 3.366750419Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.633249581, 3.366750419}Solution
x = {16.633249581, 3.366750419}
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