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Simplifying 2x(5 + x) = 15 (5 * 2x + x * 2x) = 15 (10x + 2x2) = 15 Solving 10x + 2x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 10x + 2x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 5x + x2 = 0 + 7.5 5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 5x + x2 = 7.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 7.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 7.5 + 6.25 Combine like terms: 7.5 + 6.25 = 13.75 6.25 + 5x + x2 = 13.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + 2.5) equal to 3.708099244 and -3.708099244.Subproblem 1
x + 2.5 = 3.708099244 Simplifying x + 2.5 = 3.708099244 Reorder the terms: 2.5 + x = 3.708099244 Solving 2.5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.708099244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.708099244 + -2.5 x = 3.708099244 + -2.5 Combine like terms: 3.708099244 + -2.5 = 1.208099244 x = 1.208099244 Simplifying x = 1.208099244Subproblem 2
x + 2.5 = -3.708099244 Simplifying x + 2.5 = -3.708099244 Reorder the terms: 2.5 + x = -3.708099244 Solving 2.5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.708099244 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.708099244 + -2.5 x = -3.708099244 + -2.5 Combine like terms: -3.708099244 + -2.5 = -6.208099244 x = -6.208099244 Simplifying x = -6.208099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.208099244, -6.208099244}
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