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Simplifying x(x + 4) = 71.69 Reorder the terms: x(4 + x) = 71.69 (4 * x + x * x) = 71.69 (4x + x2) = 71.69 Solving 4x + x2 = 71.69 Solving for variable 'x'. Reorder the terms: -71.69 + 4x + x2 = 71.69 + -71.69 Combine like terms: 71.69 + -71.69 = 0.00 -71.69 + 4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '71.69' to each side of the equation. -71.69 + 4x + 71.69 + x2 = 0.00 + 71.69 Reorder the terms: -71.69 + 71.69 + 4x + x2 = 0.00 + 71.69 Combine like terms: -71.69 + 71.69 = 0.00 0.00 + 4x + x2 = 0.00 + 71.69 4x + x2 = 0.00 + 71.69 Combine like terms: 0.00 + 71.69 = 71.69 4x + x2 = 71.69 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 = 71.69 + 4 Reorder the terms: 4 + 4x + x2 = 71.69 + 4 Combine like terms: 71.69 + 4 = 75.69 4 + 4x + x2 = 75.69 Factor a perfect square on the left side: (x + 2)(x + 2) = 75.69 Calculate the square root of the right side: 8.7 Break this problem into two subproblems by setting (x + 2) equal to 8.7 and -8.7.Subproblem 1
x + 2 = 8.7 Simplifying x + 2 = 8.7 Reorder the terms: 2 + x = 8.7 Solving 2 + x = 8.7 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 = 8.7 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.7 + -2 x = 8.7 + -2 Combine like terms: 8.7 + -2 = 6.7 x = 6.7 Simplifying x = 6.7Subproblem 2
x + 2 = -8.7 Simplifying x + 2 = -8.7 Reorder the terms: 2 + x = -8.7 Solving 2 + x = -8.7 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 = -8.7 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.7 + -2 x = -8.7 + -2 Combine like terms: -8.7 + -2 = -10.7 x = -10.7 Simplifying x = -10.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.7, -10.7}
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