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Simplifying X2 + -15X + 30 = 3X Reorder the terms: 30 + -15X + X2 = 3X Solving 30 + -15X + X2 = 3X Solving for variable 'X'. Reorder the terms: 30 + -15X + -3X + X2 = 3X + -3X Combine like terms: -15X + -3X = -18X 30 + -18X + X2 = 3X + -3X Combine like terms: 3X + -3X = 0 30 + -18X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -18X + -30 + X2 = 0 + -30 Reorder the terms: 30 + -30 + -18X + X2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -18X + X2 = 0 + -30 -18X + X2 = 0 + -30 Combine like terms: 0 + -30 = -30 -18X + X2 = -30 The X term is -18X. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18X + 81 + X2 = -30 + 81 Reorder the terms: 81 + -18X + X2 = -30 + 81 Combine like terms: -30 + 81 = 51 81 + -18X + X2 = 51 Factor a perfect square on the left side: (X + -9)(X + -9) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (X + -9) equal to 7.141428429 and -7.141428429.Subproblem 1
X + -9 = 7.141428429 Simplifying X + -9 = 7.141428429 Reorder the terms: -9 + X = 7.141428429 Solving -9 + X = 7.141428429 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = 7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + X = 7.141428429 + 9 X = 7.141428429 + 9 Combine like terms: 7.141428429 + 9 = 16.141428429 X = 16.141428429 Simplifying X = 16.141428429Subproblem 2
X + -9 = -7.141428429 Simplifying X + -9 = -7.141428429 Reorder the terms: -9 + X = -7.141428429 Solving -9 + X = -7.141428429 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + X = -7.141428429 + 9 Combine like terms: -9 + 9 = 0 0 + X = -7.141428429 + 9 X = -7.141428429 + 9 Combine like terms: -7.141428429 + 9 = 1.858571571 X = 1.858571571 Simplifying X = 1.858571571Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.141428429, 1.858571571}
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