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Simplifying 10x + x2 = 36 Solving 10x + x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 10x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 10x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 10x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 10x + x2 = 0 + 36 10x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 10x + x2 = 36 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 = 36 + 25 Reorder the terms: 25 + 10x + x2 = 36 + 25 Combine like terms: 36 + 25 = 61 25 + 10x + x2 = 61 Factor a perfect square on the left side: (x + 5)(x + 5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 5) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 5 = 7.810249676 Simplifying x + 5 = 7.810249676 Reorder the terms: 5 + x = 7.810249676 Solving 5 + x = 7.810249676 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 = 7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.810249676 + -5 x = 7.810249676 + -5 Combine like terms: 7.810249676 + -5 = 2.810249676 x = 2.810249676 Simplifying x = 2.810249676Subproblem 2
x + 5 = -7.810249676 Simplifying x + 5 = -7.810249676 Reorder the terms: 5 + x = -7.810249676 Solving 5 + x = -7.810249676 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 = -7.810249676 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.810249676 + -5 x = -7.810249676 + -5 Combine like terms: -7.810249676 + -5 = -12.810249676 x = -12.810249676 Simplifying x = -12.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.810249676, -12.810249676}
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