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Simplifying x2 + 4x = 62 Reorder the terms: 4x + x2 = 62 Solving 4x + x2 = 62 Solving for variable 'x'. Reorder the terms: -62 + 4x + x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -62 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 4x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 4x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 4x + x2 = 0 + 62 4x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 4x + x2 = 62 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 62 + 4 Reorder the terms: 4 + 4x + x2 = 62 + 4 Combine like terms: 62 + 4 = 66 4 + 4x + x2 = 66 Factor a perfect square on the left side: (x + 2)(x + 2) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 2) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 2 = 8.124038405 Simplifying x + 2 = 8.124038405 Reorder the terms: 2 + x = 8.124038405 Solving 2 + x = 8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.124038405 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.124038405 + -2 x = 8.124038405 + -2 Combine like terms: 8.124038405 + -2 = 6.124038405 x = 6.124038405 Simplifying x = 6.124038405Subproblem 2
x + 2 = -8.124038405 Simplifying x + 2 = -8.124038405 Reorder the terms: 2 + x = -8.124038405 Solving 2 + x = -8.124038405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.124038405 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.124038405 + -2 x = -8.124038405 + -2 Combine like terms: -8.124038405 + -2 = -10.124038405 x = -10.124038405 Simplifying x = -10.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.124038405, -10.124038405}
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