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Simplifying 192 + -28x + -4x2 = 0 Solving 192 + -28x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(48 + -7x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(48 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 48 + -7x + -1x2 = 0 Solving 48 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 7x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 7x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 7x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 7x + x2 = 0 + 48 7x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 7x + x2 = 48 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 48 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 48 + 12.25 Combine like terms: 48 + 12.25 = 60.25 12.25 + 7x + x2 = 60.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 3.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 3.5 = 7.762087348 Simplifying x + 3.5 = 7.762087348 Reorder the terms: 3.5 + x = 7.762087348 Solving 3.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.762087348 + -3.5 x = 7.762087348 + -3.5 Combine like terms: 7.762087348 + -3.5 = 4.262087348 x = 4.262087348 Simplifying x = 4.262087348Subproblem 2
x + 3.5 = -7.762087348 Simplifying x + 3.5 = -7.762087348 Reorder the terms: 3.5 + x = -7.762087348 Solving 3.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.762087348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.762087348 + -3.5 x = -7.762087348 + -3.5 Combine like terms: -7.762087348 + -3.5 = -11.262087348 x = -11.262087348 Simplifying x = -11.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.262087348, -11.262087348}Solution
x = {4.262087348, -11.262087348}
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