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Simplifying 6x2 + 21x + -200 = 0 Reorder the terms: -200 + 21x + 6x2 = 0 Solving -200 + 21x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -33.33333333 + 3.5x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 3.5x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 3.5x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 3.5x + x2 = 0 + 33.33333333 3.5x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 3.5x + x2 = 33.33333333 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 33.33333333 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 33.33333333 + 3.0625 Combine like terms: 33.33333333 + 3.0625 = 36.39583333 3.0625 + 3.5x + x2 = 36.39583333 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 36.39583333 Calculate the square root of the right side: 6.032895932 Break this problem into two subproblems by setting (x + 1.75) equal to 6.032895932 and -6.032895932.Subproblem 1
x + 1.75 = 6.032895932 Simplifying x + 1.75 = 6.032895932 Reorder the terms: 1.75 + x = 6.032895932 Solving 1.75 + x = 6.032895932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 6.032895932 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 6.032895932 + -1.75 x = 6.032895932 + -1.75 Combine like terms: 6.032895932 + -1.75 = 4.282895932 x = 4.282895932 Simplifying x = 4.282895932Subproblem 2
x + 1.75 = -6.032895932 Simplifying x + 1.75 = -6.032895932 Reorder the terms: 1.75 + x = -6.032895932 Solving 1.75 + x = -6.032895932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -6.032895932 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -6.032895932 + -1.75 x = -6.032895932 + -1.75 Combine like terms: -6.032895932 + -1.75 = -7.782895932 x = -7.782895932 Simplifying x = -7.782895932Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.282895932, -7.782895932}
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