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Simplifying 0 = x2 + 47x + -40 Reorder the terms: 0 = -40 + 47x + x2 Solving 0 = -40 + 47x + x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + -47x + -1x2 = -40 + 47x + x2 + 40 + -47x + -1x2 Reorder the terms: 40 + -47x + -1x2 = -40 + 40 + 47x + -47x + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + -47x + -1x2 = 0 + 47x + -47x + x2 + -1x2 40 + -47x + -1x2 = 47x + -47x + x2 + -1x2 Combine like terms: 47x + -47x = 0 40 + -47x + -1x2 = 0 + x2 + -1x2 40 + -47x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + -47x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 47x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 47x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 47x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 47x + x2 = 0 + 40 47x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 47x + x2 = 40 The x term is 47x. Take half its coefficient (23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. 47x + 552.25 + x2 = 40 + 552.25 Reorder the terms: 552.25 + 47x + x2 = 40 + 552.25 Combine like terms: 40 + 552.25 = 592.25 552.25 + 47x + x2 = 592.25 Factor a perfect square on the left side: (x + 23.5)(x + 23.5) = 592.25 Calculate the square root of the right side: 24.336187047 Break this problem into two subproblems by setting (x + 23.5) equal to 24.336187047 and -24.336187047.Subproblem 1
x + 23.5 = 24.336187047 Simplifying x + 23.5 = 24.336187047 Reorder the terms: 23.5 + x = 24.336187047 Solving 23.5 + x = 24.336187047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = 24.336187047 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = 24.336187047 + -23.5 x = 24.336187047 + -23.5 Combine like terms: 24.336187047 + -23.5 = 0.836187047 x = 0.836187047 Simplifying x = 0.836187047Subproblem 2
x + 23.5 = -24.336187047 Simplifying x + 23.5 = -24.336187047 Reorder the terms: 23.5 + x = -24.336187047 Solving 23.5 + x = -24.336187047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = -24.336187047 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = -24.336187047 + -23.5 x = -24.336187047 + -23.5 Combine like terms: -24.336187047 + -23.5 = -47.836187047 x = -47.836187047 Simplifying x = -47.836187047Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.836187047, -47.836187047}
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