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Simplifying 3x2 + 12x + -374 = 0 Reorder the terms: -374 + 12x + 3x2 = 0 Solving -374 + 12x + 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'. -124.6666667 + 4x + x2 = 0 Move the constant term to the right: Add '124.6666667' to each side of the equation. -124.6666667 + 4x + 124.6666667 + x2 = 0 + 124.6666667 Reorder the terms: -124.6666667 + 124.6666667 + 4x + x2 = 0 + 124.6666667 Combine like terms: -124.6666667 + 124.6666667 = 0.0000000 0.0000000 + 4x + x2 = 0 + 124.6666667 4x + x2 = 0 + 124.6666667 Combine like terms: 0 + 124.6666667 = 124.6666667 4x + x2 = 124.6666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 124.6666667 + 4 Reorder the terms: 4 + 4x + x2 = 124.6666667 + 4 Combine like terms: 124.6666667 + 4 = 128.6666667 4 + 4x + x2 = 128.6666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 128.6666667 Calculate the square root of the right side: 11.34313302 Break this problem into two subproblems by setting (x + 2) equal to 11.34313302 and -11.34313302.Subproblem 1
x + 2 = 11.34313302 Simplifying x + 2 = 11.34313302 Reorder the terms: 2 + x = 11.34313302 Solving 2 + x = 11.34313302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.34313302 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.34313302 + -2 x = 11.34313302 + -2 Combine like terms: 11.34313302 + -2 = 9.34313302 x = 9.34313302 Simplifying x = 9.34313302Subproblem 2
x + 2 = -11.34313302 Simplifying x + 2 = -11.34313302 Reorder the terms: 2 + x = -11.34313302 Solving 2 + x = -11.34313302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.34313302 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.34313302 + -2 x = -11.34313302 + -2 Combine like terms: -11.34313302 + -2 = -13.34313302 x = -13.34313302 Simplifying x = -13.34313302Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.34313302, -13.34313302}
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