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Simplifying 3x2 + -30x + 4 = 0 Reorder the terms: 4 + -30x + 3x2 = 0 Solving 4 + -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'. 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 = 23.666666667 25 + -10x + x2 = 23.666666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 23.666666667 Calculate the square root of the right side: 4.86483984 Break this problem into two subproblems by setting (x + -5) equal to 4.86483984 and -4.86483984.Subproblem 1
x + -5 = 4.86483984 Simplifying x + -5 = 4.86483984 Reorder the terms: -5 + x = 4.86483984 Solving -5 + x = 4.86483984 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 = 4.86483984 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.86483984 + 5 x = 4.86483984 + 5 Combine like terms: 4.86483984 + 5 = 9.86483984 x = 9.86483984 Simplifying x = 9.86483984Subproblem 2
x + -5 = -4.86483984 Simplifying x + -5 = -4.86483984 Reorder the terms: -5 + x = -4.86483984 Solving -5 + x = -4.86483984 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 = -4.86483984 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.86483984 + 5 x = -4.86483984 + 5 Combine like terms: -4.86483984 + 5 = 0.13516016 x = 0.13516016 Simplifying x = 0.13516016Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.86483984, 0.13516016}
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