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Simplifying 6 = (-0.25x2) + 1.7x + 3.5 Reorder the terms: 6 = 3.5 + 1.7x + (-0.25x2) Solving 6 = 3.5 + 1.7x + (-0.25x2) Solving for variable 'x'. Combine like terms: 6 + -3.5 = 2.5 2.5 + -1.7x + (0.25x2) = 3.5 + 1.7x + (-0.25x2) + -3.5 + -1.7x + (0.25x2) Reorder the terms: 2.5 + -1.7x + (0.25x2) = 3.5 + -3.5 + 1.7x + -1.7x + (-0.25x2) + (0.25x2) Combine like terms: 3.5 + -3.5 = 0.0 2.5 + -1.7x + (0.25x2) = 0.0 + 1.7x + -1.7x + (-0.25x2) + (0.25x2) 2.5 + -1.7x + (0.25x2) = 1.7x + -1.7x + (-0.25x2) + (0.25x2) Combine like terms: 1.7x + -1.7x = 0.0 2.5 + -1.7x + (0.25x2) = 0.0 + (-0.25x2) + (0.25x2) 2.5 + -1.7x + (0.25x2) = (-0.25x2) + (0.25x2) Combine like terms: (-0.25x2) + (0.25x2) = 0.00 2.5 + -1.7x + (0.25x2) = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 10 + -6.8x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -6.8x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -6.8x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -6.8x + x2 = 0 + -10 -6.8x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -6.8x + x2 = -10 The x term is -6.8x. Take half its coefficient (-3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. -6.8x + 11.56 + x2 = -10 + 11.56 Reorder the terms: 11.56 + -6.8x + x2 = -10 + 11.56 Combine like terms: -10 + 11.56 = 1.56 11.56 + -6.8x + x2 = 1.56 Factor a perfect square on the left side: ((x) + -3.4)((x) + -3.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting ((x) + -3.4) equal to 1.2489996 and -1.2489996.Subproblem 1
(x) + -3.4 = 1.2489996 Simplifying (x) + -3.4 = 1.2489996 x + -3.4 = 1.2489996 Reorder the terms: -3.4 + x = 1.2489996 Solving -3.4 + x = 1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = 1.2489996 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = 1.2489996 + 3.4 x = 1.2489996 + 3.4 Combine like terms: 1.2489996 + 3.4 = 4.6489996 x = 4.6489996 Simplifying x = 4.6489996Subproblem 2
(x) + -3.4 = -1.2489996 Simplifying (x) + -3.4 = -1.2489996 x + -3.4 = -1.2489996 Reorder the terms: -3.4 + x = -1.2489996 Solving -3.4 + x = -1.2489996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.4' to each side of the equation. -3.4 + 3.4 + x = -1.2489996 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + x = -1.2489996 + 3.4 x = -1.2489996 + 3.4 Combine like terms: -1.2489996 + 3.4 = 2.1510004 x = 2.1510004 Simplifying x = 2.1510004Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6489996, 2.1510004}
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