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Simplifying 7.61x2 + -3.73x = 7.83 Reorder the terms: -3.73x + 7.61x2 = 7.83 Solving -3.73x + 7.61x2 = 7.83 Solving for variable 'x'. Reorder the terms: -7.83 + -3.73x + 7.61x2 = 7.83 + -7.83 Combine like terms: 7.83 + -7.83 = 0.00 -7.83 + -3.73x + 7.61x2 = 0.00 Begin completing the square. Divide all terms by 7.61 the coefficient of the squared term: Divide each side by '7.61'. -1.02890933 + -0.4901445466x + x2 = 0 Move the constant term to the right: Add '1.02890933' to each side of the equation. -1.02890933 + -0.4901445466x + 1.02890933 + x2 = 0 + 1.02890933 Reorder the terms: -1.02890933 + 1.02890933 + -0.4901445466x + x2 = 0 + 1.02890933 Combine like terms: -1.02890933 + 1.02890933 = 0.00000000 0.00000000 + -0.4901445466x + x2 = 0 + 1.02890933 -0.4901445466x + x2 = 0 + 1.02890933 Combine like terms: 0 + 1.02890933 = 1.02890933 -0.4901445466x + x2 = 1.02890933 The x term is -0.4901445466x. Take half its coefficient (-0.2450722733). Square it (0.06006041914) and add it to both sides. Add '0.06006041914' to each side of the equation. -0.4901445466x + 0.06006041914 + x2 = 1.02890933 + 0.06006041914 Reorder the terms: 0.06006041914 + -0.4901445466x + x2 = 1.02890933 + 0.06006041914 Combine like terms: 1.02890933 + 0.06006041914 = 1.08896974914 0.06006041914 + -0.4901445466x + x2 = 1.08896974914 Factor a perfect square on the left side: (x + -0.2450722733)(x + -0.2450722733) = 1.08896974914 Calculate the square root of the right side: 1.043537134 Break this problem into two subproblems by setting (x + -0.2450722733) equal to 1.043537134 and -1.043537134.Subproblem 1
x + -0.2450722733 = 1.043537134 Simplifying x + -0.2450722733 = 1.043537134 Reorder the terms: -0.2450722733 + x = 1.043537134 Solving -0.2450722733 + x = 1.043537134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2450722733' to each side of the equation. -0.2450722733 + 0.2450722733 + x = 1.043537134 + 0.2450722733 Combine like terms: -0.2450722733 + 0.2450722733 = 0.0000000000 0.0000000000 + x = 1.043537134 + 0.2450722733 x = 1.043537134 + 0.2450722733 Combine like terms: 1.043537134 + 0.2450722733 = 1.2886094073 x = 1.2886094073 Simplifying x = 1.2886094073Subproblem 2
x + -0.2450722733 = -1.043537134 Simplifying x + -0.2450722733 = -1.043537134 Reorder the terms: -0.2450722733 + x = -1.043537134 Solving -0.2450722733 + x = -1.043537134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2450722733' to each side of the equation. -0.2450722733 + 0.2450722733 + x = -1.043537134 + 0.2450722733 Combine like terms: -0.2450722733 + 0.2450722733 = 0.0000000000 0.0000000000 + x = -1.043537134 + 0.2450722733 x = -1.043537134 + 0.2450722733 Combine like terms: -1.043537134 + 0.2450722733 = -0.7984648607 x = -0.7984648607 Simplifying x = -0.7984648607Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2886094073, -0.7984648607}
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