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Simplifying 133.33x2 + 10x = 6 Reorder the terms: 10x + 133.33x2 = 6 Solving 10x + 133.33x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 10x + 133.33x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 10x + 133.33x2 = 0 Begin completing the square. Divide all terms by 133.33 the coefficient of the squared term: Divide each side by '133.33'. -0.04500112503 + 0.07500187505x + x2 = 0 Move the constant term to the right: Add '0.04500112503' to each side of the equation. -0.04500112503 + 0.07500187505x + 0.04500112503 + x2 = 0 + 0.04500112503 Reorder the terms: -0.04500112503 + 0.04500112503 + 0.07500187505x + x2 = 0 + 0.04500112503 Combine like terms: -0.04500112503 + 0.04500112503 = 0.00000000000 0.00000000000 + 0.07500187505x + x2 = 0 + 0.04500112503 0.07500187505x + x2 = 0 + 0.04500112503 Combine like terms: 0 + 0.04500112503 = 0.04500112503 0.07500187505x + x2 = 0.04500112503 The x term is 0.07500187505x. Take half its coefficient (0.03750093753). Square it (0.001406320316) and add it to both sides. Add '0.001406320316' to each side of the equation. 0.07500187505x + 0.001406320316 + x2 = 0.04500112503 + 0.001406320316 Reorder the terms: 0.001406320316 + 0.07500187505x + x2 = 0.04500112503 + 0.001406320316 Combine like terms: 0.04500112503 + 0.001406320316 = 0.046407445346 0.001406320316 + 0.07500187505x + x2 = 0.046407445346 Factor a perfect square on the left side: (x + 0.03750093753)(x + 0.03750093753) = 0.046407445346 Calculate the square root of the right side: 0.215423874 Break this problem into two subproblems by setting (x + 0.03750093753) equal to 0.215423874 and -0.215423874.Subproblem 1
x + 0.03750093753 = 0.215423874 Simplifying x + 0.03750093753 = 0.215423874 Reorder the terms: 0.03750093753 + x = 0.215423874 Solving 0.03750093753 + x = 0.215423874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03750093753' to each side of the equation. 0.03750093753 + -0.03750093753 + x = 0.215423874 + -0.03750093753 Combine like terms: 0.03750093753 + -0.03750093753 = 0.00000000000 0.00000000000 + x = 0.215423874 + -0.03750093753 x = 0.215423874 + -0.03750093753 Combine like terms: 0.215423874 + -0.03750093753 = 0.17792293647 x = 0.17792293647 Simplifying x = 0.17792293647Subproblem 2
x + 0.03750093753 = -0.215423874 Simplifying x + 0.03750093753 = -0.215423874 Reorder the terms: 0.03750093753 + x = -0.215423874 Solving 0.03750093753 + x = -0.215423874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03750093753' to each side of the equation. 0.03750093753 + -0.03750093753 + x = -0.215423874 + -0.03750093753 Combine like terms: 0.03750093753 + -0.03750093753 = 0.00000000000 0.00000000000 + x = -0.215423874 + -0.03750093753 x = -0.215423874 + -0.03750093753 Combine like terms: -0.215423874 + -0.03750093753 = -0.25292481153 x = -0.25292481153 Simplifying x = -0.25292481153Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17792293647, -0.25292481153}
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