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Simplifying 2X(2X + 1) + -7 = 0 Reorder the terms: 2X(1 + 2X) + -7 = 0 (1 * 2X + 2X * 2X) + -7 = 0 (2X + 4X2) + -7 = 0 Reorder the terms: -7 + 2X + 4X2 = 0 Solving -7 + 2X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 0.5X + X2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.5X + 1.75 + X2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.5X + X2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.5X + X2 = 0 + 1.75 0.5X + X2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.5X + X2 = 1.75 The X term is 0.5X. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5X + 0.0625 + X2 = 1.75 + 0.0625 Reorder the terms: 0.0625 + 0.5X + X2 = 1.75 + 0.0625 Combine like terms: 1.75 + 0.0625 = 1.8125 0.0625 + 0.5X + X2 = 1.8125 Factor a perfect square on the left side: (X + 0.25)(X + 0.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (X + 0.25) equal to 1.346291202 and -1.346291202.Subproblem 1
X + 0.25 = 1.346291202 Simplifying X + 0.25 = 1.346291202 Reorder the terms: 0.25 + X = 1.346291202 Solving 0.25 + X = 1.346291202 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + X = 1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + X = 1.346291202 + -0.25 X = 1.346291202 + -0.25 Combine like terms: 1.346291202 + -0.25 = 1.096291202 X = 1.096291202 Simplifying X = 1.096291202Subproblem 2
X + 0.25 = -1.346291202 Simplifying X + 0.25 = -1.346291202 Reorder the terms: 0.25 + X = -1.346291202 Solving 0.25 + X = -1.346291202 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + X = -1.346291202 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + X = -1.346291202 + -0.25 X = -1.346291202 + -0.25 Combine like terms: -1.346291202 + -0.25 = -1.596291202 X = -1.596291202 Simplifying X = -1.596291202Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.096291202, -1.596291202}
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