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Simplifying (3x + -9) * x = 79 Reorder the terms: (-9 + 3x) * x = 79 Reorder the terms for easier multiplication: x(-9 + 3x) = 79 (-9 * x + 3x * x) = 79 (-9x + 3x2) = 79 Solving -9x + 3x2 = 79 Solving for variable 'x'. Reorder the terms: -79 + -9x + 3x2 = 79 + -79 Combine like terms: 79 + -79 = 0 -79 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -26.33333333 + -3x + x2 = 0 Move the constant term to the right: Add '26.33333333' to each side of the equation. -26.33333333 + -3x + 26.33333333 + x2 = 0 + 26.33333333 Reorder the terms: -26.33333333 + 26.33333333 + -3x + x2 = 0 + 26.33333333 Combine like terms: -26.33333333 + 26.33333333 = 0.00000000 0.00000000 + -3x + x2 = 0 + 26.33333333 -3x + x2 = 0 + 26.33333333 Combine like terms: 0 + 26.33333333 = 26.33333333 -3x + x2 = 26.33333333 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 = 26.33333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 26.33333333 + 2.25 Combine like terms: 26.33333333 + 2.25 = 28.58333333 2.25 + -3x + x2 = 28.58333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 28.58333333 Calculate the square root of the right side: 5.34633831 Break this problem into two subproblems by setting (x + -1.5) equal to 5.34633831 and -5.34633831.Subproblem 1
x + -1.5 = 5.34633831 Simplifying x + -1.5 = 5.34633831 Reorder the terms: -1.5 + x = 5.34633831 Solving -1.5 + x = 5.34633831 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 = 5.34633831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.34633831 + 1.5 x = 5.34633831 + 1.5 Combine like terms: 5.34633831 + 1.5 = 6.84633831 x = 6.84633831 Simplifying x = 6.84633831Subproblem 2
x + -1.5 = -5.34633831 Simplifying x + -1.5 = -5.34633831 Reorder the terms: -1.5 + x = -5.34633831 Solving -1.5 + x = -5.34633831 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 = -5.34633831 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.34633831 + 1.5 x = -5.34633831 + 1.5 Combine like terms: -5.34633831 + 1.5 = -3.84633831 x = -3.84633831 Simplifying x = -3.84633831Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.84633831, -3.84633831}
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