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Simplifying x2 + -10x = 37 Reorder the terms: -10x + x2 = 37 Solving -10x + x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + -10x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -10x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -10x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -10x + x2 = 0 + 37 -10x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -10x + x2 = 37 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 37 + 25 Reorder the terms: 25 + -10x + x2 = 37 + 25 Combine like terms: 37 + 25 = 62 25 + -10x + x2 = 62 Factor a perfect square on the left side: (x + -5)(x + -5) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + -5) equal to 7.874007874 and -7.874007874.Subproblem 1
x + -5 = 7.874007874 Simplifying x + -5 = 7.874007874 Reorder the terms: -5 + x = 7.874007874 Solving -5 + x = 7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.874007874 + 5 x = 7.874007874 + 5 Combine like terms: 7.874007874 + 5 = 12.874007874 x = 12.874007874 Simplifying x = 12.874007874Subproblem 2
x + -5 = -7.874007874 Simplifying x + -5 = -7.874007874 Reorder the terms: -5 + x = -7.874007874 Solving -5 + x = -7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.874007874 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.874007874 + 5 x = -7.874007874 + 5 Combine like terms: -7.874007874 + 5 = -2.874007874 x = -2.874007874 Simplifying x = -2.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.874007874, -2.874007874}
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