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Simplifying 408 = 49.4x + 4x + x2 Combine like terms: 49.4x + 4x = 53.4x 408 = 53.4x + x2 Solving 408 = 53.4x + x2 Solving for variable 'x'. Reorder the terms: 408 + -53.4x + -1x2 = 53.4x + -53.4x + x2 + -1x2 Combine like terms: 53.4x + -53.4x = 0.0 408 + -53.4x + -1x2 = 0.0 + x2 + -1x2 408 + -53.4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 408 + -53.4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -408 + 53.4x + x2 = 0 Move the constant term to the right: Add '408' to each side of the equation. -408 + 53.4x + 408 + x2 = 0 + 408 Reorder the terms: -408 + 408 + 53.4x + x2 = 0 + 408 Combine like terms: -408 + 408 = 0 0 + 53.4x + x2 = 0 + 408 53.4x + x2 = 0 + 408 Combine like terms: 0 + 408 = 408 53.4x + x2 = 408 The x term is 53.4x. Take half its coefficient (26.7). Square it (712.89) and add it to both sides. Add '712.89' to each side of the equation. 53.4x + 712.89 + x2 = 408 + 712.89 Reorder the terms: 712.89 + 53.4x + x2 = 408 + 712.89 Combine like terms: 408 + 712.89 = 1120.89 712.89 + 53.4x + x2 = 1120.89 Factor a perfect square on the left side: (x + 26.7)(x + 26.7) = 1120.89 Calculate the square root of the right side: 33.479695339 Break this problem into two subproblems by setting (x + 26.7) equal to 33.479695339 and -33.479695339.Subproblem 1
x + 26.7 = 33.479695339 Simplifying x + 26.7 = 33.479695339 Reorder the terms: 26.7 + x = 33.479695339 Solving 26.7 + x = 33.479695339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.7' to each side of the equation. 26.7 + -26.7 + x = 33.479695339 + -26.7 Combine like terms: 26.7 + -26.7 = 0.0 0.0 + x = 33.479695339 + -26.7 x = 33.479695339 + -26.7 Combine like terms: 33.479695339 + -26.7 = 6.779695339 x = 6.779695339 Simplifying x = 6.779695339Subproblem 2
x + 26.7 = -33.479695339 Simplifying x + 26.7 = -33.479695339 Reorder the terms: 26.7 + x = -33.479695339 Solving 26.7 + x = -33.479695339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.7' to each side of the equation. 26.7 + -26.7 + x = -33.479695339 + -26.7 Combine like terms: 26.7 + -26.7 = 0.0 0.0 + x = -33.479695339 + -26.7 x = -33.479695339 + -26.7 Combine like terms: -33.479695339 + -26.7 = -60.179695339 x = -60.179695339 Simplifying x = -60.179695339Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.779695339, -60.179695339}
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