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Simplifying (x)(x + 4) = 142.5 Reorder the terms: x(4 + x) = 142.5 (4 * x + x * x) = 142.5 (4x + x2) = 142.5 Solving 4x + x2 = 142.5 Solving for variable 'x'. Reorder the terms: -142.5 + 4x + x2 = 142.5 + -142.5 Combine like terms: 142.5 + -142.5 = 0.0 -142.5 + 4x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '142.5' to each side of the equation. -142.5 + 4x + 142.5 + x2 = 0.0 + 142.5 Reorder the terms: -142.5 + 142.5 + 4x + x2 = 0.0 + 142.5 Combine like terms: -142.5 + 142.5 = 0.0 0.0 + 4x + x2 = 0.0 + 142.5 4x + x2 = 0.0 + 142.5 Combine like terms: 0.0 + 142.5 = 142.5 4x + x2 = 142.5 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 = 142.5 + 4 Reorder the terms: 4 + 4x + x2 = 142.5 + 4 Combine like terms: 142.5 + 4 = 146.5 4 + 4x + x2 = 146.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 146.5 Calculate the square root of the right side: 12.103718437 Break this problem into two subproblems by setting (x + 2) equal to 12.103718437 and -12.103718437.Subproblem 1
x + 2 = 12.103718437 Simplifying x + 2 = 12.103718437 Reorder the terms: 2 + x = 12.103718437 Solving 2 + x = 12.103718437 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 = 12.103718437 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.103718437 + -2 x = 12.103718437 + -2 Combine like terms: 12.103718437 + -2 = 10.103718437 x = 10.103718437 Simplifying x = 10.103718437Subproblem 2
x + 2 = -12.103718437 Simplifying x + 2 = -12.103718437 Reorder the terms: 2 + x = -12.103718437 Solving 2 + x = -12.103718437 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 = -12.103718437 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.103718437 + -2 x = -12.103718437 + -2 Combine like terms: -12.103718437 + -2 = -14.103718437 x = -14.103718437 Simplifying x = -14.103718437Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.103718437, -14.103718437}
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