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Simplifying 3x(x + -3) = 25 Reorder the terms: 3x(-3 + x) = 25 (-3 * 3x + x * 3x) = 25 (-9x + 3x2) = 25 Solving -9x + 3x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -9x + 3x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8.333333333 + -3x + x2 = 0 Move the constant term to the right: Add '8.333333333' to each side of the equation. -8.333333333 + -3x + 8.333333333 + x2 = 0 + 8.333333333 Reorder the terms: -8.333333333 + 8.333333333 + -3x + x2 = 0 + 8.333333333 Combine like terms: -8.333333333 + 8.333333333 = 0.000000000 0.000000000 + -3x + x2 = 0 + 8.333333333 -3x + x2 = 0 + 8.333333333 Combine like terms: 0 + 8.333333333 = 8.333333333 -3x + x2 = 8.333333333 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 = 8.333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8.333333333 + 2.25 Combine like terms: 8.333333333 + 2.25 = 10.583333333 2.25 + -3x + x2 = 10.583333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.583333333 Calculate the square root of the right side: 3.253203549 Break this problem into two subproblems by setting (x + -1.5) equal to 3.253203549 and -3.253203549.Subproblem 1
x + -1.5 = 3.253203549 Simplifying x + -1.5 = 3.253203549 Reorder the terms: -1.5 + x = 3.253203549 Solving -1.5 + x = 3.253203549 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 = 3.253203549 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.253203549 + 1.5 x = 3.253203549 + 1.5 Combine like terms: 3.253203549 + 1.5 = 4.753203549 x = 4.753203549 Simplifying x = 4.753203549Subproblem 2
x + -1.5 = -3.253203549 Simplifying x + -1.5 = -3.253203549 Reorder the terms: -1.5 + x = -3.253203549 Solving -1.5 + x = -3.253203549 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 = -3.253203549 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.253203549 + 1.5 x = -3.253203549 + 1.5 Combine like terms: -3.253203549 + 1.5 = -1.753203549 x = -1.753203549 Simplifying x = -1.753203549Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.753203549, -1.753203549}
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