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Simplifying 3x(15 + -1x) = 65 (15 * 3x + -1x * 3x) = 65 (45x + -3x2) = 65 Solving 45x + -3x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 45x + -3x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 45x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 21.66666667 + -15x + x2 = 0 Move the constant term to the right: Add '-21.66666667' to each side of the equation. 21.66666667 + -15x + -21.66666667 + x2 = 0 + -21.66666667 Reorder the terms: 21.66666667 + -21.66666667 + -15x + x2 = 0 + -21.66666667 Combine like terms: 21.66666667 + -21.66666667 = 0.00000000 0.00000000 + -15x + x2 = 0 + -21.66666667 -15x + x2 = 0 + -21.66666667 Combine like terms: 0 + -21.66666667 = -21.66666667 -15x + x2 = -21.66666667 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -21.66666667 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -21.66666667 + 56.25 Combine like terms: -21.66666667 + 56.25 = 34.58333333 56.25 + -15x + x2 = 34.58333333 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 34.58333333 Calculate the square root of the right side: 5.880759588 Break this problem into two subproblems by setting (x + -7.5) equal to 5.880759588 and -5.880759588.Subproblem 1
x + -7.5 = 5.880759588 Simplifying x + -7.5 = 5.880759588 Reorder the terms: -7.5 + x = 5.880759588 Solving -7.5 + x = 5.880759588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.880759588 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.880759588 + 7.5 x = 5.880759588 + 7.5 Combine like terms: 5.880759588 + 7.5 = 13.380759588 x = 13.380759588 Simplifying x = 13.380759588Subproblem 2
x + -7.5 = -5.880759588 Simplifying x + -7.5 = -5.880759588 Reorder the terms: -7.5 + x = -5.880759588 Solving -7.5 + x = -5.880759588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.880759588 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.880759588 + 7.5 x = -5.880759588 + 7.5 Combine like terms: -5.880759588 + 7.5 = 1.619240412 x = 1.619240412 Simplifying x = 1.619240412Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.380759588, 1.619240412}
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