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Simplifying x2 + 7x + 2.25 = 4 Reorder the terms: 2.25 + 7x + x2 = 4 Solving 2.25 + 7x + x2 = 4 Solving for variable 'x'. Reorder the terms: 2.25 + -4 + 7x + x2 = 4 + -4 Combine like terms: 2.25 + -4 = -1.75 -1.75 + 7x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1.75 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 7x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 7x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 7x + x2 = 0 + 1.75 7x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 7x + x2 = 1.75 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 1.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 1.75 + 12.25 Combine like terms: 1.75 + 12.25 = 14 12.25 + 7x + x2 = 14 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 3.5) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 3.5 = 3.741657387 Simplifying x + 3.5 = 3.741657387 Reorder the terms: 3.5 + x = 3.741657387 Solving 3.5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.741657387 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.741657387 + -3.5 x = 3.741657387 + -3.5 Combine like terms: 3.741657387 + -3.5 = 0.241657387 x = 0.241657387 Simplifying x = 0.241657387Subproblem 2
x + 3.5 = -3.741657387 Simplifying x + 3.5 = -3.741657387 Reorder the terms: 3.5 + x = -3.741657387 Solving 3.5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.741657387 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.741657387 + -3.5 x = -3.741657387 + -3.5 Combine like terms: -3.741657387 + -3.5 = -7.241657387 x = -7.241657387 Simplifying x = -7.241657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.241657387, -7.241657387}
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