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Simplifying (x2) + 10x = 37 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 = 2.874007874 x = 2.874007874 Simplifying x = 2.874007874Subproblem 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 = -12.874007874 x = -12.874007874 Simplifying x = -12.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.874007874, -12.874007874}
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