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Simplifying -2x2 + 24x = 71 Reorder the terms: 24x + -2x2 = 71 Solving 24x + -2x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + 24x + -2x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 24x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 35.5 + -12x + x2 = 0 Move the constant term to the right: Add '-35.5' to each side of the equation. 35.5 + -12x + -35.5 + x2 = 0 + -35.5 Reorder the terms: 35.5 + -35.5 + -12x + x2 = 0 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + -12x + x2 = 0 + -35.5 -12x + x2 = 0 + -35.5 Combine like terms: 0 + -35.5 = -35.5 -12x + x2 = -35.5 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 = -35.5 + 36 Reorder the terms: 36 + -12x + x2 = -35.5 + 36 Combine like terms: -35.5 + 36 = 0.5 36 + -12x + x2 = 0.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -6) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -6 = 0.707106781 Simplifying x + -6 = 0.707106781 Reorder the terms: -6 + x = 0.707106781 Solving -6 + x = 0.707106781 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 = 0.707106781 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0.707106781 + 6 x = 0.707106781 + 6 Combine like terms: 0.707106781 + 6 = 6.707106781 x = 6.707106781 Simplifying x = 6.707106781Subproblem 2
x + -6 = -0.707106781 Simplifying x + -6 = -0.707106781 Reorder the terms: -6 + x = -0.707106781 Solving -6 + x = -0.707106781 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 = -0.707106781 + 6 Combine like terms: -6 + 6 = 0 0 + x = -0.707106781 + 6 x = -0.707106781 + 6 Combine like terms: -0.707106781 + 6 = 5.292893219 x = 5.292893219 Simplifying x = 5.292893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.707106781, 5.292893219}
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