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Simplifying 403 = x(x + 5) Reorder the terms: 403 = x(5 + x) 403 = (5 * x + x * x) 403 = (5x + x2) Solving 403 = 5x + x2 Solving for variable 'x'. Reorder the terms: 403 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 403 + -5x + -1x2 = 0 + x2 + -1x2 403 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 403 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -403 + 5x + x2 = 0 Move the constant term to the right: Add '403' to each side of the equation. -403 + 5x + 403 + x2 = 0 + 403 Reorder the terms: -403 + 403 + 5x + x2 = 0 + 403 Combine like terms: -403 + 403 = 0 0 + 5x + x2 = 0 + 403 5x + x2 = 0 + 403 Combine like terms: 0 + 403 = 403 5x + x2 = 403 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 = 403 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 403 + 6.25 Combine like terms: 403 + 6.25 = 409.25 6.25 + 5x + x2 = 409.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 409.25 Calculate the square root of the right side: 20.229928324 Break this problem into two subproblems by setting (x + 2.5) equal to 20.229928324 and -20.229928324.Subproblem 1
x + 2.5 = 20.229928324 Simplifying x + 2.5 = 20.229928324 Reorder the terms: 2.5 + x = 20.229928324 Solving 2.5 + x = 20.229928324 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 = 20.229928324 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 20.229928324 + -2.5 x = 20.229928324 + -2.5 Combine like terms: 20.229928324 + -2.5 = 17.729928324 x = 17.729928324 Simplifying x = 17.729928324Subproblem 2
x + 2.5 = -20.229928324 Simplifying x + 2.5 = -20.229928324 Reorder the terms: 2.5 + x = -20.229928324 Solving 2.5 + x = -20.229928324 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 = -20.229928324 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -20.229928324 + -2.5 x = -20.229928324 + -2.5 Combine like terms: -20.229928324 + -2.5 = -22.729928324 x = -22.729928324 Simplifying x = -22.729928324Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.729928324, -22.729928324}
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