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Simplifying 4x2 + -96x + 160 = 0 Reorder the terms: 160 + -96x + 4x2 = 0 Solving 160 + -96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(40 + -24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(40 + -24x + x2)' equal to zero and attempt to solve: Simplifying 40 + -24x + x2 = 0 Solving 40 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -24x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -24x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -24x + x2 = 0 + -40 -24x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -24x + x2 = -40 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -40 + 144 Reorder the terms: 144 + -24x + x2 = -40 + 144 Combine like terms: -40 + 144 = 104 144 + -24x + x2 = 104 Factor a perfect square on the left side: (x + -12)(x + -12) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + -12) equal to 10.198039027 and -10.198039027.Subproblem 1
x + -12 = 10.198039027 Simplifying x + -12 = 10.198039027 Reorder the terms: -12 + x = 10.198039027 Solving -12 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 10.198039027 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.198039027 + 12 x = 10.198039027 + 12 Combine like terms: 10.198039027 + 12 = 22.198039027 x = 22.198039027 Simplifying x = 22.198039027Subproblem 2
x + -12 = -10.198039027 Simplifying x + -12 = -10.198039027 Reorder the terms: -12 + x = -10.198039027 Solving -12 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -10.198039027 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.198039027 + 12 x = -10.198039027 + 12 Combine like terms: -10.198039027 + 12 = 1.801960973 x = 1.801960973 Simplifying x = 1.801960973Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.198039027, 1.801960973}Solution
x = {22.198039027, 1.801960973}
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