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Simplifying x(x + 4) = 112.5 Reorder the terms: x(4 + x) = 112.5 (4 * x + x * x) = 112.5 (4x + x2) = 112.5 Solving 4x + x2 = 112.5 Solving for variable 'x'. Reorder the terms: -112.5 + 4x + x2 = 112.5 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 -112.5 + 4x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 4x + 112.5 + x2 = 0.0 + 112.5 Reorder the terms: -112.5 + 112.5 + 4x + x2 = 0.0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 4x + x2 = 0.0 + 112.5 4x + x2 = 0.0 + 112.5 Combine like terms: 0.0 + 112.5 = 112.5 4x + x2 = 112.5 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 = 112.5 + 4 Reorder the terms: 4 + 4x + x2 = 112.5 + 4 Combine like terms: 112.5 + 4 = 116.5 4 + 4x + x2 = 116.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 116.5 Calculate the square root of the right side: 10.793516572 Break this problem into two subproblems by setting (x + 2) equal to 10.793516572 and -10.793516572.Subproblem 1
x + 2 = 10.793516572 Simplifying x + 2 = 10.793516572 Reorder the terms: 2 + x = 10.793516572 Solving 2 + x = 10.793516572 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 = 10.793516572 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.793516572 + -2 x = 10.793516572 + -2 Combine like terms: 10.793516572 + -2 = 8.793516572 x = 8.793516572 Simplifying x = 8.793516572Subproblem 2
x + 2 = -10.793516572 Simplifying x + 2 = -10.793516572 Reorder the terms: 2 + x = -10.793516572 Solving 2 + x = -10.793516572 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 = -10.793516572 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.793516572 + -2 x = -10.793516572 + -2 Combine like terms: -10.793516572 + -2 = -12.793516572 x = -12.793516572 Simplifying x = -12.793516572Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.793516572, -12.793516572}
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