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Simplifying -3x2 + 30x + -16 = 0 Reorder the terms: -16 + 30x + -3x2 = 0 Solving -16 + 30x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.333333333 + -10x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -10x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -10x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -10x + x2 = 0 + -5.333333333 -10x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -10x + x2 = -5.333333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -5.333333333 + 25 Reorder the terms: 25 + -10x + x2 = -5.333333333 + 25 Combine like terms: -5.333333333 + 25 = 19.666666667 25 + -10x + x2 = 19.666666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 19.666666667 Calculate the square root of the right side: 4.434711565 Break this problem into two subproblems by setting (x + -5) equal to 4.434711565 and -4.434711565.Subproblem 1
x + -5 = 4.434711565 Simplifying x + -5 = 4.434711565 Reorder the terms: -5 + x = 4.434711565 Solving -5 + x = 4.434711565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.434711565 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.434711565 + 5 x = 4.434711565 + 5 Combine like terms: 4.434711565 + 5 = 9.434711565 x = 9.434711565 Simplifying x = 9.434711565Subproblem 2
x + -5 = -4.434711565 Simplifying x + -5 = -4.434711565 Reorder the terms: -5 + x = -4.434711565 Solving -5 + x = -4.434711565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.434711565 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.434711565 + 5 x = -4.434711565 + 5 Combine like terms: -4.434711565 + 5 = 0.565288435 x = 0.565288435 Simplifying x = 0.565288435Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.434711565, 0.565288435}
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