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Simplifying x2 + 7x = 190 Reorder the terms: 7x + x2 = 190 Solving 7x + x2 = 190 Solving for variable 'x'. Reorder the terms: -190 + 7x + x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -190 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + 7x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 7x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 7x + x2 = 0 + 190 7x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 7x + x2 = 190 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 = 190 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 190 + 12.25 Combine like terms: 190 + 12.25 = 202.25 12.25 + 7x + x2 = 202.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + 3.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + 3.5 = 14.221462653 Simplifying x + 3.5 = 14.221462653 Reorder the terms: 3.5 + x = 14.221462653 Solving 3.5 + x = 14.221462653 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 = 14.221462653 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 14.221462653 + -3.5 x = 14.221462653 + -3.5 Combine like terms: 14.221462653 + -3.5 = 10.721462653 x = 10.721462653 Simplifying x = 10.721462653Subproblem 2
x + 3.5 = -14.221462653 Simplifying x + 3.5 = -14.221462653 Reorder the terms: 3.5 + x = -14.221462653 Solving 3.5 + x = -14.221462653 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 = -14.221462653 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -14.221462653 + -3.5 x = -14.221462653 + -3.5 Combine like terms: -14.221462653 + -3.5 = -17.721462653 x = -17.721462653 Simplifying x = -17.721462653Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.721462653, -17.721462653}
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