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Simplifying 3x2 + -30x + -13 = 0 Reorder the terms: -13 + -30x + 3x2 = 0 Solving -13 + -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'. -4.333333333 + -10x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -10x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -10x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -10x + x2 = 0 + 4.333333333 -10x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -10x + x2 = 4.333333333 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 = 4.333333333 + 25 Reorder the terms: 25 + -10x + x2 = 4.333333333 + 25 Combine like terms: 4.333333333 + 25 = 29.333333333 25 + -10x + x2 = 29.333333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 29.333333333 Calculate the square root of the right side: 5.416025603 Break this problem into two subproblems by setting (x + -5) equal to 5.416025603 and -5.416025603.Subproblem 1
x + -5 = 5.416025603 Simplifying x + -5 = 5.416025603 Reorder the terms: -5 + x = 5.416025603 Solving -5 + x = 5.416025603 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 = 5.416025603 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.416025603 + 5 x = 5.416025603 + 5 Combine like terms: 5.416025603 + 5 = 10.416025603 x = 10.416025603 Simplifying x = 10.416025603Subproblem 2
x + -5 = -5.416025603 Simplifying x + -5 = -5.416025603 Reorder the terms: -5 + x = -5.416025603 Solving -5 + x = -5.416025603 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 = -5.416025603 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.416025603 + 5 x = -5.416025603 + 5 Combine like terms: -5.416025603 + 5 = -0.416025603 x = -0.416025603 Simplifying x = -0.416025603Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.416025603, -0.416025603}
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