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Simplifying 57x + -78 = x2 Reorder the terms: -78 + 57x = x2 Solving -78 + 57x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -78 + 57x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 78 + -57x + x2 = 0 Move the constant term to the right: Add '-78' to each side of the equation. 78 + -57x + -78 + x2 = 0 + -78 Reorder the terms: 78 + -78 + -57x + x2 = 0 + -78 Combine like terms: 78 + -78 = 0 0 + -57x + x2 = 0 + -78 -57x + x2 = 0 + -78 Combine like terms: 0 + -78 = -78 -57x + x2 = -78 The x term is -57x. Take half its coefficient (-28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. -57x + 812.25 + x2 = -78 + 812.25 Reorder the terms: 812.25 + -57x + x2 = -78 + 812.25 Combine like terms: -78 + 812.25 = 734.25 812.25 + -57x + x2 = 734.25 Factor a perfect square on the left side: (x + -28.5)(x + -28.5) = 734.25 Calculate the square root of the right side: 27.09704781 Break this problem into two subproblems by setting (x + -28.5) equal to 27.09704781 and -27.09704781.Subproblem 1
x + -28.5 = 27.09704781 Simplifying x + -28.5 = 27.09704781 Reorder the terms: -28.5 + x = 27.09704781 Solving -28.5 + x = 27.09704781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 27.09704781 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 27.09704781 + 28.5 x = 27.09704781 + 28.5 Combine like terms: 27.09704781 + 28.5 = 55.59704781 x = 55.59704781 Simplifying x = 55.59704781Subproblem 2
x + -28.5 = -27.09704781 Simplifying x + -28.5 = -27.09704781 Reorder the terms: -28.5 + x = -27.09704781 Solving -28.5 + x = -27.09704781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -27.09704781 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -27.09704781 + 28.5 x = -27.09704781 + 28.5 Combine like terms: -27.09704781 + 28.5 = 1.40295219 x = 1.40295219 Simplifying x = 1.40295219Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.59704781, 1.40295219}
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