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Simplifying -5.7x(x + 9.2) + 4.1 = 3.4 + -6.9x Reorder the terms: -5.7x(9.2 + x) + 4.1 = 3.4 + -6.9x (9.2 * -5.7x + x * -5.7x) + 4.1 = 3.4 + -6.9x (-52.44x + -5.7x2) + 4.1 = 3.4 + -6.9x Reorder the terms: 4.1 + -52.44x + -5.7x2 = 3.4 + -6.9x Solving 4.1 + -52.44x + -5.7x2 = 3.4 + -6.9x Solving for variable 'x'. Reorder the terms: 4.1 + -3.4 + -52.44x + 6.9x + -5.7x2 = 3.4 + -6.9x + -3.4 + 6.9x Combine like terms: 4.1 + -3.4 = 0.7 0.7 + -52.44x + 6.9x + -5.7x2 = 3.4 + -6.9x + -3.4 + 6.9x Combine like terms: -52.44x + 6.9x = -45.54x 0.7 + -45.54x + -5.7x2 = 3.4 + -6.9x + -3.4 + 6.9x Reorder the terms: 0.7 + -45.54x + -5.7x2 = 3.4 + -3.4 + -6.9x + 6.9x Combine like terms: 3.4 + -3.4 = 0.0 0.7 + -45.54x + -5.7x2 = 0.0 + -6.9x + 6.9x 0.7 + -45.54x + -5.7x2 = -6.9x + 6.9x Combine like terms: -6.9x + 6.9x = 0.0 0.7 + -45.54x + -5.7x2 = 0.0 Begin completing the square. Divide all terms by -5.7 the coefficient of the squared term: Divide each side by '-5.7'. -0.1228070175 + 7.989473684x + x2 = 0 Move the constant term to the right: Add '0.1228070175' to each side of the equation. -0.1228070175 + 7.989473684x + 0.1228070175 + x2 = 0 + 0.1228070175 Reorder the terms: -0.1228070175 + 0.1228070175 + 7.989473684x + x2 = 0 + 0.1228070175 Combine like terms: -0.1228070175 + 0.1228070175 = 0.0000000000 0.0000000000 + 7.989473684x + x2 = 0 + 0.1228070175 7.989473684x + x2 = 0 + 0.1228070175 Combine like terms: 0 + 0.1228070175 = 0.1228070175 7.989473684x + x2 = 0.1228070175 The x term is 7.989473684x. Take half its coefficient (3.994736842). Square it (15.95792244) and add it to both sides. Add '15.95792244' to each side of the equation. 7.989473684x + 15.95792244 + x2 = 0.1228070175 + 15.95792244 Reorder the terms: 15.95792244 + 7.989473684x + x2 = 0.1228070175 + 15.95792244 Combine like terms: 0.1228070175 + 15.95792244 = 16.0807294575 15.95792244 + 7.989473684x + x2 = 16.0807294575 Factor a perfect square on the left side: (x + 3.994736842)(x + 3.994736842) = 16.0807294575 Calculate the square root of the right side: 4.010078485 Break this problem into two subproblems by setting (x + 3.994736842) equal to 4.010078485 and -4.010078485.Subproblem 1
x + 3.994736842 = 4.010078485 Simplifying x + 3.994736842 = 4.010078485 Reorder the terms: 3.994736842 + x = 4.010078485 Solving 3.994736842 + x = 4.010078485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.994736842' to each side of the equation. 3.994736842 + -3.994736842 + x = 4.010078485 + -3.994736842 Combine like terms: 3.994736842 + -3.994736842 = 0.000000000 0.000000000 + x = 4.010078485 + -3.994736842 x = 4.010078485 + -3.994736842 Combine like terms: 4.010078485 + -3.994736842 = 0.015341643 x = 0.015341643 Simplifying x = 0.015341643Subproblem 2
x + 3.994736842 = -4.010078485 Simplifying x + 3.994736842 = -4.010078485 Reorder the terms: 3.994736842 + x = -4.010078485 Solving 3.994736842 + x = -4.010078485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.994736842' to each side of the equation. 3.994736842 + -3.994736842 + x = -4.010078485 + -3.994736842 Combine like terms: 3.994736842 + -3.994736842 = 0.000000000 0.000000000 + x = -4.010078485 + -3.994736842 x = -4.010078485 + -3.994736842 Combine like terms: -4.010078485 + -3.994736842 = -8.004815327 x = -8.004815327 Simplifying x = -8.004815327Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.015341643, -8.004815327}
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