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Simplifying 10x2 + 69.44 = 68.4x Reorder the terms: 69.44 + 10x2 = 68.4x Solving 69.44 + 10x2 = 68.4x Solving for variable 'x'. Reorder the terms: 69.44 + -68.4x + 10x2 = 68.4x + -68.4x Combine like terms: 68.4x + -68.4x = 0.0 69.44 + -68.4x + 10x2 = 0.0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 6.944 + -6.84x + x2 = 0.0 Move the constant term to the right: Add '-6.944' to each side of the equation. 6.944 + -6.84x + -6.944 + x2 = 0.0 + -6.944 Reorder the terms: 6.944 + -6.944 + -6.84x + x2 = 0.0 + -6.944 Combine like terms: 6.944 + -6.944 = 0.000 0.000 + -6.84x + x2 = 0.0 + -6.944 -6.84x + x2 = 0.0 + -6.944 Combine like terms: 0.0 + -6.944 = -6.944 -6.84x + x2 = -6.944 The x term is -6.84x. Take half its coefficient (-3.42). Square it (11.6964) and add it to both sides. Add '11.6964' to each side of the equation. -6.84x + 11.6964 + x2 = -6.944 + 11.6964 Reorder the terms: 11.6964 + -6.84x + x2 = -6.944 + 11.6964 Combine like terms: -6.944 + 11.6964 = 4.7524 11.6964 + -6.84x + x2 = 4.7524 Factor a perfect square on the left side: (x + -3.42)(x + -3.42) = 4.7524 Calculate the square root of the right side: 2.18 Break this problem into two subproblems by setting (x + -3.42) equal to 2.18 and -2.18.Subproblem 1
x + -3.42 = 2.18 Simplifying x + -3.42 = 2.18 Reorder the terms: -3.42 + x = 2.18 Solving -3.42 + x = 2.18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.42' to each side of the equation. -3.42 + 3.42 + x = 2.18 + 3.42 Combine like terms: -3.42 + 3.42 = 0.00 0.00 + x = 2.18 + 3.42 x = 2.18 + 3.42 Combine like terms: 2.18 + 3.42 = 5.6 x = 5.6 Simplifying x = 5.6Subproblem 2
x + -3.42 = -2.18 Simplifying x + -3.42 = -2.18 Reorder the terms: -3.42 + x = -2.18 Solving -3.42 + x = -2.18 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.42' to each side of the equation. -3.42 + 3.42 + x = -2.18 + 3.42 Combine like terms: -3.42 + 3.42 = 0.00 0.00 + x = -2.18 + 3.42 x = -2.18 + 3.42 Combine like terms: -2.18 + 3.42 = 1.24 x = 1.24 Simplifying x = 1.24Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.6, 1.24}
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