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Simplifying 4x + 169 = -2x2 + 48x Reorder the terms: 169 + 4x = -2x2 + 48x Reorder the terms: 169 + 4x = 48x + -2x2 Solving 169 + 4x = 48x + -2x2 Solving for variable 'x'. Combine like terms: 4x + -48x = -44x 169 + -44x + 2x2 = 48x + -2x2 + -48x + 2x2 Reorder the terms: 169 + -44x + 2x2 = 48x + -48x + -2x2 + 2x2 Combine like terms: 48x + -48x = 0 169 + -44x + 2x2 = 0 + -2x2 + 2x2 169 + -44x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 169 + -44x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 84.5 + -22x + x2 = 0 Move the constant term to the right: Add '-84.5' to each side of the equation. 84.5 + -22x + -84.5 + x2 = 0 + -84.5 Reorder the terms: 84.5 + -84.5 + -22x + x2 = 0 + -84.5 Combine like terms: 84.5 + -84.5 = 0.0 0.0 + -22x + x2 = 0 + -84.5 -22x + x2 = 0 + -84.5 Combine like terms: 0 + -84.5 = -84.5 -22x + x2 = -84.5 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -84.5 + 121 Reorder the terms: 121 + -22x + x2 = -84.5 + 121 Combine like terms: -84.5 + 121 = 36.5 121 + -22x + x2 = 36.5 Factor a perfect square on the left side: (x + -11)(x + -11) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x + -11) equal to 6.041522987 and -6.041522987.Subproblem 1
x + -11 = 6.041522987 Simplifying x + -11 = 6.041522987 Reorder the terms: -11 + x = 6.041522987 Solving -11 + x = 6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 6.041522987 + 11 Combine like terms: -11 + 11 = 0 0 + x = 6.041522987 + 11 x = 6.041522987 + 11 Combine like terms: 6.041522987 + 11 = 17.041522987 x = 17.041522987 Simplifying x = 17.041522987Subproblem 2
x + -11 = -6.041522987 Simplifying x + -11 = -6.041522987 Reorder the terms: -11 + x = -6.041522987 Solving -11 + x = -6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -6.041522987 + 11 Combine like terms: -11 + 11 = 0 0 + x = -6.041522987 + 11 x = -6.041522987 + 11 Combine like terms: -6.041522987 + 11 = 4.958477013 x = 4.958477013 Simplifying x = 4.958477013Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.041522987, 4.958477013}
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