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Simplifying 2x2 + 19x = 174 Reorder the terms: 19x + 2x2 = 174 Solving 19x + 2x2 = 174 Solving for variable 'x'. Reorder the terms: -174 + 19x + 2x2 = 174 + -174 Combine like terms: 174 + -174 = 0 -174 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87 + 9.5x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + 9.5x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 9.5x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 9.5x + x2 = 0 + 87 9.5x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 9.5x + x2 = 87 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 87 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 87 + 22.5625 Combine like terms: 87 + 22.5625 = 109.5625 22.5625 + 9.5x + x2 = 109.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 109.5625 Calculate the square root of the right side: 10.467210708 Break this problem into two subproblems by setting (x + 4.75) equal to 10.467210708 and -10.467210708.Subproblem 1
x + 4.75 = 10.467210708 Simplifying x + 4.75 = 10.467210708 Reorder the terms: 4.75 + x = 10.467210708 Solving 4.75 + x = 10.467210708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 10.467210708 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 10.467210708 + -4.75 x = 10.467210708 + -4.75 Combine like terms: 10.467210708 + -4.75 = 5.717210708 x = 5.717210708 Simplifying x = 5.717210708Subproblem 2
x + 4.75 = -10.467210708 Simplifying x + 4.75 = -10.467210708 Reorder the terms: 4.75 + x = -10.467210708 Solving 4.75 + x = -10.467210708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -10.467210708 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -10.467210708 + -4.75 x = -10.467210708 + -4.75 Combine like terms: -10.467210708 + -4.75 = -15.217210708 x = -15.217210708 Simplifying x = -15.217210708Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.717210708, -15.217210708}
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