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Simplifying 40 = 7x + x2 Solving 40 = 7x + x2 Solving for variable 'x'. Reorder the terms: 40 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 40 + -7x + -1x2 = 0 + x2 + -1x2 40 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 7x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 7x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 7x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 7x + x2 = 0 + 40 7x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 7x + x2 = 40 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 40 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 40 + 12.25 Combine like terms: 40 + 12.25 = 52.25 12.25 + 7x + x2 = 52.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 3.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 3.5 = 7.228416147 Simplifying x + 3.5 = 7.228416147 Reorder the terms: 3.5 + x = 7.228416147 Solving 3.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.228416147 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.228416147 + -3.5 x = 7.228416147 + -3.5 Combine like terms: 7.228416147 + -3.5 = 3.728416147 x = 3.728416147 Simplifying x = 3.728416147Subproblem 2
x + 3.5 = -7.228416147 Simplifying x + 3.5 = -7.228416147 Reorder the terms: 3.5 + x = -7.228416147 Solving 3.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.228416147 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.228416147 + -3.5 x = -7.228416147 + -3.5 Combine like terms: -7.228416147 + -3.5 = -10.728416147 x = -10.728416147 Simplifying x = -10.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.728416147, -10.728416147}
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