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Simplifying 7 + -5X = X2 Solving 7 + -5X = X2 Solving for variable 'X'. Combine like terms: X2 + -1X2 = 0 7 + -5X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 5X + X2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 5X + 7 + X2 = 0 + 7 Reorder the terms: -7 + 7 + 5X + X2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5X + X2 = 0 + 7 5X + X2 = 0 + 7 Combine like terms: 0 + 7 = 7 5X + X2 = 7 The X term is 5X. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5X + 6.25 + X2 = 7 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + 5X + X2 = 13.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (X + 2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
X + 2.5 = 3.640054945 Simplifying X + 2.5 = 3.640054945 Reorder the terms: 2.5 + X = 3.640054945 Solving 2.5 + X = 3.640054945 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 3.640054945 + -2.5 X = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 X = 1.140054945 Simplifying X = 1.140054945Subproblem 2
X + 2.5 = -3.640054945 Simplifying X + 2.5 = -3.640054945 Reorder the terms: 2.5 + X = -3.640054945 Solving 2.5 + X = -3.640054945 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -3.640054945 + -2.5 X = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 X = -6.140054945 Simplifying X = -6.140054945Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.140054945, -6.140054945}
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