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Simplifying 133.33x2 + 50x = 6 Reorder the terms: 50x + 133.33x2 = 6 Solving 50x + 133.33x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 50x + 133.33x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 50x + 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 + 0.3750093752x + x2 = 0 Move the constant term to the right: Add '0.04500112503' to each side of the equation. -0.04500112503 + 0.3750093752x + 0.04500112503 + x2 = 0 + 0.04500112503 Reorder the terms: -0.04500112503 + 0.04500112503 + 0.3750093752x + x2 = 0 + 0.04500112503 Combine like terms: -0.04500112503 + 0.04500112503 = 0.00000000000 0.00000000000 + 0.3750093752x + x2 = 0 + 0.04500112503 0.3750093752x + x2 = 0 + 0.04500112503 Combine like terms: 0 + 0.04500112503 = 0.04500112503 0.3750093752x + x2 = 0.04500112503 The x term is 0.3750093752x. Take half its coefficient (0.1875046876). Square it (0.03515800787) and add it to both sides. Add '0.03515800787' to each side of the equation. 0.3750093752x + 0.03515800787 + x2 = 0.04500112503 + 0.03515800787 Reorder the terms: 0.03515800787 + 0.3750093752x + x2 = 0.04500112503 + 0.03515800787 Combine like terms: 0.04500112503 + 0.03515800787 = 0.0801591329 0.03515800787 + 0.3750093752x + x2 = 0.0801591329 Factor a perfect square on the left side: (x + 0.1875046876)(x + 0.1875046876) = 0.0801591329 Calculate the square root of the right side: 0.283123883 Break this problem into two subproblems by setting (x + 0.1875046876) equal to 0.283123883 and -0.283123883.Subproblem 1
x + 0.1875046876 = 0.283123883 Simplifying x + 0.1875046876 = 0.283123883 Reorder the terms: 0.1875046876 + x = 0.283123883 Solving 0.1875046876 + x = 0.283123883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875046876' to each side of the equation. 0.1875046876 + -0.1875046876 + x = 0.283123883 + -0.1875046876 Combine like terms: 0.1875046876 + -0.1875046876 = 0.0000000000 0.0000000000 + x = 0.283123883 + -0.1875046876 x = 0.283123883 + -0.1875046876 Combine like terms: 0.283123883 + -0.1875046876 = 0.0956191954 x = 0.0956191954 Simplifying x = 0.0956191954Subproblem 2
x + 0.1875046876 = -0.283123883 Simplifying x + 0.1875046876 = -0.283123883 Reorder the terms: 0.1875046876 + x = -0.283123883 Solving 0.1875046876 + x = -0.283123883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875046876' to each side of the equation. 0.1875046876 + -0.1875046876 + x = -0.283123883 + -0.1875046876 Combine like terms: 0.1875046876 + -0.1875046876 = 0.0000000000 0.0000000000 + x = -0.283123883 + -0.1875046876 x = -0.283123883 + -0.1875046876 Combine like terms: -0.283123883 + -0.1875046876 = -0.4706285706 x = -0.4706285706 Simplifying x = -0.4706285706Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0956191954, -0.4706285706}
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