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Simplifying x(x + 3) = 125 Reorder the terms: x(3 + x) = 125 (3 * x + x * x) = 125 (3x + x2) = 125 Solving 3x + x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 3x + x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 3x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 3x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 3x + x2 = 0 + 125 3x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 3x + x2 = 125 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 125 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 125 + 2.25 Combine like terms: 125 + 2.25 = 127.25 2.25 + 3x + x2 = 127.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 127.25 Calculate the square root of the right side: 11.280514173 Break this problem into two subproblems by setting (x + 1.5) equal to 11.280514173 and -11.280514173.Subproblem 1
x + 1.5 = 11.280514173 Simplifying x + 1.5 = 11.280514173 Reorder the terms: 1.5 + x = 11.280514173 Solving 1.5 + x = 11.280514173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.280514173 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.280514173 + -1.5 x = 11.280514173 + -1.5 Combine like terms: 11.280514173 + -1.5 = 9.780514173 x = 9.780514173 Simplifying x = 9.780514173Subproblem 2
x + 1.5 = -11.280514173 Simplifying x + 1.5 = -11.280514173 Reorder the terms: 1.5 + x = -11.280514173 Solving 1.5 + x = -11.280514173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.280514173 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.280514173 + -1.5 x = -11.280514173 + -1.5 Combine like terms: -11.280514173 + -1.5 = -12.780514173 x = -12.780514173 Simplifying x = -12.780514173Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.780514173, -12.780514173}
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