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Simplifying X2 + -2 * 6X = 36 + 25 Multiply -2 * 6 X2 + -12X = 36 + 25 Reorder the terms: -12X + X2 = 36 + 25 Combine like terms: 36 + 25 = 61 -12X + X2 = 61 Solving -12X + X2 = 61 Solving for variable 'X'. Reorder the terms: -61 + -12X + X2 = 61 + -61 Combine like terms: 61 + -61 = 0 -61 + -12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + -12X + 61 + X2 = 0 + 61 Reorder the terms: -61 + 61 + -12X + X2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -12X + X2 = 0 + 61 -12X + X2 = 0 + 61 Combine like terms: 0 + 61 = 61 -12X + X2 = 61 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = 61 + 36 Reorder the terms: 36 + -12X + X2 = 61 + 36 Combine like terms: 61 + 36 = 97 36 + -12X + X2 = 97 Factor a perfect square on the left side: (X + -6)(X + -6) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (X + -6) equal to 9.848857802 and -9.848857802.Subproblem 1
X + -6 = 9.848857802 Simplifying X + -6 = 9.848857802 Reorder the terms: -6 + X = 9.848857802 Solving -6 + X = 9.848857802 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 9.848857802 + 6 Combine like terms: -6 + 6 = 0 0 + X = 9.848857802 + 6 X = 9.848857802 + 6 Combine like terms: 9.848857802 + 6 = 15.848857802 X = 15.848857802 Simplifying X = 15.848857802Subproblem 2
X + -6 = -9.848857802 Simplifying X + -6 = -9.848857802 Reorder the terms: -6 + X = -9.848857802 Solving -6 + X = -9.848857802 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -9.848857802 + 6 Combine like terms: -6 + 6 = 0 0 + X = -9.848857802 + 6 X = -9.848857802 + 6 Combine like terms: -9.848857802 + 6 = -3.848857802 X = -3.848857802 Simplifying X = -3.848857802Solution
The solution to the problem is based on the solutions from the subproblems. X = {15.848857802, -3.848857802}
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