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Simplifying x(x + 60) = 142 Reorder the terms: x(60 + x) = 142 (60 * x + x * x) = 142 (60x + x2) = 142 Solving 60x + x2 = 142 Solving for variable 'x'. Reorder the terms: -142 + 60x + x2 = 142 + -142 Combine like terms: 142 + -142 = 0 -142 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '142' to each side of the equation. -142 + 60x + 142 + x2 = 0 + 142 Reorder the terms: -142 + 142 + 60x + x2 = 0 + 142 Combine like terms: -142 + 142 = 0 0 + 60x + x2 = 0 + 142 60x + x2 = 0 + 142 Combine like terms: 0 + 142 = 142 60x + x2 = 142 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 142 + 900 Reorder the terms: 900 + 60x + x2 = 142 + 900 Combine like terms: 142 + 900 = 1042 900 + 60x + x2 = 1042 Factor a perfect square on the left side: (x + 30)(x + 30) = 1042 Calculate the square root of the right side: 32.280024783 Break this problem into two subproblems by setting (x + 30) equal to 32.280024783 and -32.280024783.Subproblem 1
x + 30 = 32.280024783 Simplifying x + 30 = 32.280024783 Reorder the terms: 30 + x = 32.280024783 Solving 30 + x = 32.280024783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 32.280024783 + -30 Combine like terms: 30 + -30 = 0 0 + x = 32.280024783 + -30 x = 32.280024783 + -30 Combine like terms: 32.280024783 + -30 = 2.280024783 x = 2.280024783 Simplifying x = 2.280024783Subproblem 2
x + 30 = -32.280024783 Simplifying x + 30 = -32.280024783 Reorder the terms: 30 + x = -32.280024783 Solving 30 + x = -32.280024783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -32.280024783 + -30 Combine like terms: 30 + -30 = 0 0 + x = -32.280024783 + -30 x = -32.280024783 + -30 Combine like terms: -32.280024783 + -30 = -62.280024783 x = -62.280024783 Simplifying x = -62.280024783Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.280024783, -62.280024783}
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