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Simplifying 6x2 + 3x + -320 = 0 Reorder the terms: -320 + 3x + 6x2 = 0 Solving -320 + 3x + 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'. -53.33333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '53.33333333' to each side of the equation. -53.33333333 + 0.5x + 53.33333333 + x2 = 0 + 53.33333333 Reorder the terms: -53.33333333 + 53.33333333 + 0.5x + x2 = 0 + 53.33333333 Combine like terms: -53.33333333 + 53.33333333 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 53.33333333 0.5x + x2 = 0 + 53.33333333 Combine like terms: 0 + 53.33333333 = 53.33333333 0.5x + x2 = 53.33333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 53.33333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 53.33333333 + 0.0625 Combine like terms: 53.33333333 + 0.0625 = 53.39583333 0.0625 + 0.5x + x2 = 53.39583333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 53.39583333 Calculate the square root of the right side: 7.307245263 Break this problem into two subproblems by setting (x + 0.25) equal to 7.307245263 and -7.307245263.Subproblem 1
x + 0.25 = 7.307245263 Simplifying x + 0.25 = 7.307245263 Reorder the terms: 0.25 + x = 7.307245263 Solving 0.25 + x = 7.307245263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 7.307245263 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 7.307245263 + -0.25 x = 7.307245263 + -0.25 Combine like terms: 7.307245263 + -0.25 = 7.057245263 x = 7.057245263 Simplifying x = 7.057245263Subproblem 2
x + 0.25 = -7.307245263 Simplifying x + 0.25 = -7.307245263 Reorder the terms: 0.25 + x = -7.307245263 Solving 0.25 + x = -7.307245263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -7.307245263 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -7.307245263 + -0.25 x = -7.307245263 + -0.25 Combine like terms: -7.307245263 + -0.25 = -7.557245263 x = -7.557245263 Simplifying x = -7.557245263Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.057245263, -7.557245263}
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