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Simplifying 3x(x + 3) = 8 Reorder the terms: 3x(3 + x) = 8 (3 * 3x + x * 3x) = 8 (9x + 3x2) = 8 Solving 9x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 9x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 3x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 3x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 3x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 3x + x2 = 0 + 2.666666667 3x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 3x + x2 = 2.666666667 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.666666667 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.666666667 + 2.25 Combine like terms: 2.666666667 + 2.25 = 4.916666667 2.25 + 3x + x2 = 4.916666667 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (x + 1.5) equal to 2.217355783 and -2.217355783.Subproblem 1
x + 1.5 = 2.217355783 Simplifying x + 1.5 = 2.217355783 Reorder the terms: 1.5 + x = 2.217355783 Solving 1.5 + x = 2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.217355783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.217355783 + -1.5 x = 2.217355783 + -1.5 Combine like terms: 2.217355783 + -1.5 = 0.717355783 x = 0.717355783 Simplifying x = 0.717355783Subproblem 2
x + 1.5 = -2.217355783 Simplifying x + 1.5 = -2.217355783 Reorder the terms: 1.5 + x = -2.217355783 Solving 1.5 + x = -2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.217355783 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.217355783 + -1.5 x = -2.217355783 + -1.5 Combine like terms: -2.217355783 + -1.5 = -3.717355783 x = -3.717355783 Simplifying x = -3.717355783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.717355783, -3.717355783}
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