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Simplifying 4x2 + -48x + 141 = 0 Reorder the terms: 141 + -48x + 4x2 = 0 Solving 141 + -48x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 35.25 + -12x + x2 = 0 Move the constant term to the right: Add '-35.25' to each side of the equation. 35.25 + -12x + -35.25 + x2 = 0 + -35.25 Reorder the terms: 35.25 + -35.25 + -12x + x2 = 0 + -35.25 Combine like terms: 35.25 + -35.25 = 0.00 0.00 + -12x + x2 = 0 + -35.25 -12x + x2 = 0 + -35.25 Combine like terms: 0 + -35.25 = -35.25 -12x + x2 = -35.25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -35.25 + 36 Reorder the terms: 36 + -12x + x2 = -35.25 + 36 Combine like terms: -35.25 + 36 = 0.75 36 + -12x + x2 = 0.75 Factor a perfect square on the left side: (x + -6)(x + -6) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -6) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -6 = 0.866025404 Simplifying x + -6 = 0.866025404 Reorder the terms: -6 + x = 0.866025404 Solving -6 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0.866025404 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0.866025404 + 6 x = 0.866025404 + 6 Combine like terms: 0.866025404 + 6 = 6.866025404 x = 6.866025404 Simplifying x = 6.866025404Subproblem 2
x + -6 = -0.866025404 Simplifying x + -6 = -0.866025404 Reorder the terms: -6 + x = -0.866025404 Solving -6 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -0.866025404 + 6 Combine like terms: -6 + 6 = 0 0 + x = -0.866025404 + 6 x = -0.866025404 + 6 Combine like terms: -0.866025404 + 6 = 5.133974596 x = 5.133974596 Simplifying x = 5.133974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.866025404, 5.133974596}
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