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Simplifying 4x2 + -176x + 10 = 0 Reorder the terms: 10 + -176x + 4x2 = 0 Solving 10 + -176x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -88x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -88x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + -88x + 2x2 = 0 Solving 5 + -88x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -44x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -44x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -44x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -44x + x2 = 0 + -2.5 -44x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -44x + x2 = -2.5 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -2.5 + 484 Reorder the terms: 484 + -44x + x2 = -2.5 + 484 Combine like terms: -2.5 + 484 = 481.5 484 + -44x + x2 = 481.5 Factor a perfect square on the left side: (x + -22)(x + -22) = 481.5 Calculate the square root of the right side: 21.943108257 Break this problem into two subproblems by setting (x + -22) equal to 21.943108257 and -21.943108257.Subproblem 1
x + -22 = 21.943108257 Simplifying x + -22 = 21.943108257 Reorder the terms: -22 + x = 21.943108257 Solving -22 + x = 21.943108257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 21.943108257 + 22 Combine like terms: -22 + 22 = 0 0 + x = 21.943108257 + 22 x = 21.943108257 + 22 Combine like terms: 21.943108257 + 22 = 43.943108257 x = 43.943108257 Simplifying x = 43.943108257Subproblem 2
x + -22 = -21.943108257 Simplifying x + -22 = -21.943108257 Reorder the terms: -22 + x = -21.943108257 Solving -22 + x = -21.943108257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -21.943108257 + 22 Combine like terms: -22 + 22 = 0 0 + x = -21.943108257 + 22 x = -21.943108257 + 22 Combine like terms: -21.943108257 + 22 = 0.056891743 x = 0.056891743 Simplifying x = 0.056891743Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.943108257, 0.056891743}Solution
x = {43.943108257, 0.056891743}
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