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Simplifying 2x(x + 3) = 25 Reorder the terms: 2x(3 + x) = 25 (3 * 2x + x * 2x) = 25 (6x + 2x2) = 25 Solving 6x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 6x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 3x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 3x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 3x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 3x + x2 = 0 + 12.5 3x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 3x + x2 = 12.5 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 = 12.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 12.5 + 2.25 Combine like terms: 12.5 + 2.25 = 14.75 2.25 + 3x + x2 = 14.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + 1.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + 1.5 = 3.840572874 Simplifying x + 1.5 = 3.840572874 Reorder the terms: 1.5 + x = 3.840572874 Solving 1.5 + x = 3.840572874 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 = 3.840572874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.840572874 + -1.5 x = 3.840572874 + -1.5 Combine like terms: 3.840572874 + -1.5 = 2.340572874 x = 2.340572874 Simplifying x = 2.340572874Subproblem 2
x + 1.5 = -3.840572874 Simplifying x + 1.5 = -3.840572874 Reorder the terms: 1.5 + x = -3.840572874 Solving 1.5 + x = -3.840572874 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 = -3.840572874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.840572874 + -1.5 x = -3.840572874 + -1.5 Combine like terms: -3.840572874 + -1.5 = -5.340572874 x = -5.340572874 Simplifying x = -5.340572874Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.340572874, -5.340572874}
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