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Simplifying 1629 = 53.4x + x2 Solving 1629 = 53.4x + x2 Solving for variable 'x'. Reorder the terms: 1629 + -53.4x + -1x2 = 53.4x + -53.4x + x2 + -1x2 Combine like terms: 53.4x + -53.4x = 0.0 1629 + -53.4x + -1x2 = 0.0 + x2 + -1x2 1629 + -53.4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1629 + -53.4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1629 + 53.4x + x2 = 0 Move the constant term to the right: Add '1629' to each side of the equation. -1629 + 53.4x + 1629 + x2 = 0 + 1629 Reorder the terms: -1629 + 1629 + 53.4x + x2 = 0 + 1629 Combine like terms: -1629 + 1629 = 0 0 + 53.4x + x2 = 0 + 1629 53.4x + x2 = 0 + 1629 Combine like terms: 0 + 1629 = 1629 53.4x + x2 = 1629 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 = 1629 + 712.89 Reorder the terms: 712.89 + 53.4x + x2 = 1629 + 712.89 Combine like terms: 1629 + 712.89 = 2341.89 712.89 + 53.4x + x2 = 2341.89 Factor a perfect square on the left side: (x + 26.7)(x + 26.7) = 2341.89 Calculate the square root of the right side: 48.393078017 Break this problem into two subproblems by setting (x + 26.7) equal to 48.393078017 and -48.393078017.Subproblem 1
x + 26.7 = 48.393078017 Simplifying x + 26.7 = 48.393078017 Reorder the terms: 26.7 + x = 48.393078017 Solving 26.7 + x = 48.393078017 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 = 48.393078017 + -26.7 Combine like terms: 26.7 + -26.7 = 0.0 0.0 + x = 48.393078017 + -26.7 x = 48.393078017 + -26.7 Combine like terms: 48.393078017 + -26.7 = 21.693078017 x = 21.693078017 Simplifying x = 21.693078017Subproblem 2
x + 26.7 = -48.393078017 Simplifying x + 26.7 = -48.393078017 Reorder the terms: 26.7 + x = -48.393078017 Solving 26.7 + x = -48.393078017 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 = -48.393078017 + -26.7 Combine like terms: 26.7 + -26.7 = 0.0 0.0 + x = -48.393078017 + -26.7 x = -48.393078017 + -26.7 Combine like terms: -48.393078017 + -26.7 = -75.093078017 x = -75.093078017 Simplifying x = -75.093078017Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.693078017, -75.093078017}
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