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Simplifying 40 = x(x + 10) Reorder the terms: 40 = x(10 + x) 40 = (10 * x + x * x) 40 = (10x + x2) Solving 40 = 10x + x2 Solving for variable 'x'. Reorder the terms: 40 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 40 + -10x + -1x2 = 0 + x2 + -1x2 40 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 10x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 10x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 10x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 10x + x2 = 0 + 40 10x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 10x + x2 = 40 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 40 + 25 Reorder the terms: 25 + 10x + x2 = 40 + 25 Combine like terms: 40 + 25 = 65 25 + 10x + x2 = 65 Factor a perfect square on the left side: (x + 5)(x + 5) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 5) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 5 = 8.062257748 Simplifying x + 5 = 8.062257748 Reorder the terms: 5 + x = 8.062257748 Solving 5 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.062257748 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.062257748 + -5 x = 8.062257748 + -5 Combine like terms: 8.062257748 + -5 = 3.062257748 x = 3.062257748 Simplifying x = 3.062257748Subproblem 2
x + 5 = -8.062257748 Simplifying x + 5 = -8.062257748 Reorder the terms: 5 + x = -8.062257748 Solving 5 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.062257748 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.062257748 + -5 x = -8.062257748 + -5 Combine like terms: -8.062257748 + -5 = -13.062257748 x = -13.062257748 Simplifying x = -13.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.062257748, -13.062257748}
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