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Simplifying x + x(x + 3 * 2) = 675 Multiply 3 * 2 x + x(x + 6) = 675 Reorder the terms: x + x(6 + x) = 675 x + (6 * x + x * x) = 675 x + (6x + x2) = 675 Combine like terms: x + 6x = 7x 7x + x2 = 675 Solving 7x + x2 = 675 Solving for variable 'x'. Reorder the terms: -675 + 7x + x2 = 675 + -675 Combine like terms: 675 + -675 = 0 -675 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '675' to each side of the equation. -675 + 7x + 675 + x2 = 0 + 675 Reorder the terms: -675 + 675 + 7x + x2 = 0 + 675 Combine like terms: -675 + 675 = 0 0 + 7x + x2 = 0 + 675 7x + x2 = 0 + 675 Combine like terms: 0 + 675 = 675 7x + x2 = 675 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 = 675 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 675 + 12.25 Combine like terms: 675 + 12.25 = 687.25 12.25 + 7x + x2 = 687.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 687.25 Calculate the square root of the right side: 26.215453458 Break this problem into two subproblems by setting (x + 3.5) equal to 26.215453458 and -26.215453458.Subproblem 1
x + 3.5 = 26.215453458 Simplifying x + 3.5 = 26.215453458 Reorder the terms: 3.5 + x = 26.215453458 Solving 3.5 + x = 26.215453458 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 = 26.215453458 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 26.215453458 + -3.5 x = 26.215453458 + -3.5 Combine like terms: 26.215453458 + -3.5 = 22.715453458 x = 22.715453458 Simplifying x = 22.715453458Subproblem 2
x + 3.5 = -26.215453458 Simplifying x + 3.5 = -26.215453458 Reorder the terms: 3.5 + x = -26.215453458 Solving 3.5 + x = -26.215453458 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 = -26.215453458 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -26.215453458 + -3.5 x = -26.215453458 + -3.5 Combine like terms: -26.215453458 + -3.5 = -29.715453458 x = -29.715453458 Simplifying x = -29.715453458Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.715453458, -29.715453458}
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