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Simplifying 3x2 + -30x = 4 Reorder the terms: -30x + 3x2 = 4 Solving -30x + 3x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -30x + 3x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -10x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -10x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -10x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -10x + x2 = 0 + 1.333333333 -10x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -10x + x2 = 1.333333333 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 = 1.333333333 + 25 Reorder the terms: 25 + -10x + x2 = 1.333333333 + 25 Combine like terms: 1.333333333 + 25 = 26.333333333 25 + -10x + x2 = 26.333333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 26.333333333 Calculate the square root of the right side: 5.131601439 Break this problem into two subproblems by setting (x + -5) equal to 5.131601439 and -5.131601439.Subproblem 1
x + -5 = 5.131601439 Simplifying x + -5 = 5.131601439 Reorder the terms: -5 + x = 5.131601439 Solving -5 + x = 5.131601439 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 = 5.131601439 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.131601439 + 5 x = 5.131601439 + 5 Combine like terms: 5.131601439 + 5 = 10.131601439 x = 10.131601439 Simplifying x = 10.131601439Subproblem 2
x + -5 = -5.131601439 Simplifying x + -5 = -5.131601439 Reorder the terms: -5 + x = -5.131601439 Solving -5 + x = -5.131601439 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 = -5.131601439 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.131601439 + 5 x = -5.131601439 + 5 Combine like terms: -5.131601439 + 5 = -0.131601439 x = -0.131601439 Simplifying x = -0.131601439Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.131601439, -0.131601439}
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