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Simplifying x2 + -7x + 10 = 37 Reorder the terms: 10 + -7x + x2 = 37 Solving 10 + -7x + x2 = 37 Solving for variable 'x'. Reorder the terms: 10 + -37 + -7x + x2 = 37 + -37 Combine like terms: 10 + -37 = -27 -27 + -7x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -27 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -7x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -7x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -7x + x2 = 0 + 27 -7x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -7x + x2 = 27 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 = 27 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 27 + 12.25 Combine like terms: 27 + 12.25 = 39.25 12.25 + -7x + x2 = 39.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -3.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -3.5 = 6.264982043 Simplifying x + -3.5 = 6.264982043 Reorder the terms: -3.5 + x = 6.264982043 Solving -3.5 + x = 6.264982043 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 = 6.264982043 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.264982043 + 3.5 x = 6.264982043 + 3.5 Combine like terms: 6.264982043 + 3.5 = 9.764982043 x = 9.764982043 Simplifying x = 9.764982043Subproblem 2
x + -3.5 = -6.264982043 Simplifying x + -3.5 = -6.264982043 Reorder the terms: -3.5 + x = -6.264982043 Solving -3.5 + x = -6.264982043 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 = -6.264982043 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.264982043 + 3.5 x = -6.264982043 + 3.5 Combine like terms: -6.264982043 + 3.5 = -2.764982043 x = -2.764982043 Simplifying x = -2.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.764982043, -2.764982043}
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