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Simplifying 2X2 + 7X = 42 Reorder the terms: 7X + 2X2 = 42 Solving 7X + 2X2 = 42 Solving for variable 'X'. Reorder the terms: -42 + 7X + 2X2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 7X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + 3.5X + X2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 3.5X + 21 + X2 = 0 + 21 Reorder the terms: -21 + 21 + 3.5X + X2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 3.5X + X2 = 0 + 21 3.5X + X2 = 0 + 21 Combine like terms: 0 + 21 = 21 3.5X + X2 = 21 The X term is 3.5X. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5X + 3.0625 + X2 = 21 + 3.0625 Reorder the terms: 3.0625 + 3.5X + X2 = 21 + 3.0625 Combine like terms: 21 + 3.0625 = 24.0625 3.0625 + 3.5X + X2 = 24.0625 Factor a perfect square on the left side: (X + 1.75)(X + 1.75) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (X + 1.75) equal to 4.905354218 and -4.905354218.Subproblem 1
X + 1.75 = 4.905354218 Simplifying X + 1.75 = 4.905354218 Reorder the terms: 1.75 + X = 4.905354218 Solving 1.75 + X = 4.905354218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + X = 4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + X = 4.905354218 + -1.75 X = 4.905354218 + -1.75 Combine like terms: 4.905354218 + -1.75 = 3.155354218 X = 3.155354218 Simplifying X = 3.155354218Subproblem 2
X + 1.75 = -4.905354218 Simplifying X + 1.75 = -4.905354218 Reorder the terms: 1.75 + X = -4.905354218 Solving 1.75 + X = -4.905354218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + X = -4.905354218 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + X = -4.905354218 + -1.75 X = -4.905354218 + -1.75 Combine like terms: -4.905354218 + -1.75 = -6.655354218 X = -6.655354218 Simplifying X = -6.655354218Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.155354218, -6.655354218}
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