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Simplifying 6x2 + -30x + 5 = 0 Reorder the terms: 5 + -30x + 6x2 = 0 Solving 5 + -30x + 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'. 0.8333333333 + -5x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -5x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -5x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + -0.8333333333 -5x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -5x + x2 = -0.8333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.8333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.8333333333 + 6.25 Combine like terms: -0.8333333333 + 6.25 = 5.4166666667 6.25 + -5x + x2 = 5.4166666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.4166666667 Calculate the square root of the right side: 2.327373341 Break this problem into two subproblems by setting (x + -2.5) equal to 2.327373341 and -2.327373341.Subproblem 1
x + -2.5 = 2.327373341 Simplifying x + -2.5 = 2.327373341 Reorder the terms: -2.5 + x = 2.327373341 Solving -2.5 + x = 2.327373341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.327373341 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.327373341 + 2.5 x = 2.327373341 + 2.5 Combine like terms: 2.327373341 + 2.5 = 4.827373341 x = 4.827373341 Simplifying x = 4.827373341Subproblem 2
x + -2.5 = -2.327373341 Simplifying x + -2.5 = -2.327373341 Reorder the terms: -2.5 + x = -2.327373341 Solving -2.5 + x = -2.327373341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.327373341 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.327373341 + 2.5 x = -2.327373341 + 2.5 Combine like terms: -2.327373341 + 2.5 = 0.172626659 x = 0.172626659 Simplifying x = 0.172626659Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.827373341, 0.172626659}
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