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Simplifying x2 + x2 + 1 + x + x2 + 4 + 4x = 194 Reorder the terms: 1 + 4 + x + 4x + x2 + x2 + x2 = 194 Combine like terms: 1 + 4 = 5 5 + x + 4x + x2 + x2 + x2 = 194 Combine like terms: x + 4x = 5x 5 + 5x + x2 + x2 + x2 = 194 Combine like terms: x2 + x2 = 2x2 5 + 5x + 2x2 + x2 = 194 Combine like terms: 2x2 + x2 = 3x2 5 + 5x + 3x2 = 194 Solving 5 + 5x + 3x2 = 194 Solving for variable 'x'. Reorder the terms: 5 + -194 + 5x + 3x2 = 194 + -194 Combine like terms: 5 + -194 = -189 -189 + 5x + 3x2 = 194 + -194 Combine like terms: 194 + -194 = 0 -189 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -63 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 1.666666667x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 1.666666667x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 1.666666667x + x2 = 0 + 63 1.666666667x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 1.666666667x + x2 = 63 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 63 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 63 + 0.6944444447 Combine like terms: 63 + 0.6944444447 = 63.6944444447 0.6944444447 + 1.666666667x + x2 = 63.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 63.6944444447 Calculate the square root of the right side: 7.980879929 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 7.980879929 and -7.980879929.Subproblem 1
x + 0.8333333335 = 7.980879929 Simplifying x + 0.8333333335 = 7.980879929 Reorder the terms: 0.8333333335 + x = 7.980879929 Solving 0.8333333335 + x = 7.980879929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 7.980879929 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 7.980879929 + -0.8333333335 x = 7.980879929 + -0.8333333335 Combine like terms: 7.980879929 + -0.8333333335 = 7.1475465955 x = 7.1475465955 Simplifying x = 7.1475465955Subproblem 2
x + 0.8333333335 = -7.980879929 Simplifying x + 0.8333333335 = -7.980879929 Reorder the terms: 0.8333333335 + x = -7.980879929 Solving 0.8333333335 + x = -7.980879929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -7.980879929 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -7.980879929 + -0.8333333335 x = -7.980879929 + -0.8333333335 Combine like terms: -7.980879929 + -0.8333333335 = -8.8142132625 x = -8.8142132625 Simplifying x = -8.8142132625Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.1475465955, -8.8142132625}
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