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Simplifying 3x(x + 5) = 10 Reorder the terms: 3x(5 + x) = 10 (5 * 3x + x * 3x) = 10 (15x + 3x2) = 10 Solving 15x + 3x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 15x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 5x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 5x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 5x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 5x + x2 = 0 + 3.333333333 5x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 5x + x2 = 3.333333333 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 = 3.333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 3.333333333 + 6.25 Combine like terms: 3.333333333 + 6.25 = 9.583333333 6.25 + 5x + x2 = 9.583333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 9.583333333 Calculate the square root of the right side: 3.095695937 Break this problem into two subproblems by setting (x + 2.5) equal to 3.095695937 and -3.095695937.Subproblem 1
x + 2.5 = 3.095695937 Simplifying x + 2.5 = 3.095695937 Reorder the terms: 2.5 + x = 3.095695937 Solving 2.5 + x = 3.095695937 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 = 3.095695937 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.095695937 + -2.5 x = 3.095695937 + -2.5 Combine like terms: 3.095695937 + -2.5 = 0.595695937 x = 0.595695937 Simplifying x = 0.595695937Subproblem 2
x + 2.5 = -3.095695937 Simplifying x + 2.5 = -3.095695937 Reorder the terms: 2.5 + x = -3.095695937 Solving 2.5 + x = -3.095695937 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 = -3.095695937 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.095695937 + -2.5 x = -3.095695937 + -2.5 Combine like terms: -3.095695937 + -2.5 = -5.595695937 x = -5.595695937 Simplifying x = -5.595695937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.595695937, -5.595695937}
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