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Simplifying 5x2 + -78x + 252 = 0 Reorder the terms: 252 + -78x + 5x2 = 0 Solving 252 + -78x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 50.4 + -15.6x + x2 = 0 Move the constant term to the right: Add '-50.4' to each side of the equation. 50.4 + -15.6x + -50.4 + x2 = 0 + -50.4 Reorder the terms: 50.4 + -50.4 + -15.6x + x2 = 0 + -50.4 Combine like terms: 50.4 + -50.4 = 0.0 0.0 + -15.6x + x2 = 0 + -50.4 -15.6x + x2 = 0 + -50.4 Combine like terms: 0 + -50.4 = -50.4 -15.6x + x2 = -50.4 The x term is -15.6x. Take half its coefficient (-7.8). Square it (60.84) and add it to both sides. Add '60.84' to each side of the equation. -15.6x + 60.84 + x2 = -50.4 + 60.84 Reorder the terms: 60.84 + -15.6x + x2 = -50.4 + 60.84 Combine like terms: -50.4 + 60.84 = 10.44 60.84 + -15.6x + x2 = 10.44 Factor a perfect square on the left side: (x + -7.8)(x + -7.8) = 10.44 Calculate the square root of the right side: 3.231098884 Break this problem into two subproblems by setting (x + -7.8) equal to 3.231098884 and -3.231098884.Subproblem 1
x + -7.8 = 3.231098884 Simplifying x + -7.8 = 3.231098884 Reorder the terms: -7.8 + x = 3.231098884 Solving -7.8 + x = 3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.8' to each side of the equation. -7.8 + 7.8 + x = 3.231098884 + 7.8 Combine like terms: -7.8 + 7.8 = 0.0 0.0 + x = 3.231098884 + 7.8 x = 3.231098884 + 7.8 Combine like terms: 3.231098884 + 7.8 = 11.031098884 x = 11.031098884 Simplifying x = 11.031098884Subproblem 2
x + -7.8 = -3.231098884 Simplifying x + -7.8 = -3.231098884 Reorder the terms: -7.8 + x = -3.231098884 Solving -7.8 + x = -3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.8' to each side of the equation. -7.8 + 7.8 + x = -3.231098884 + 7.8 Combine like terms: -7.8 + 7.8 = 0.0 0.0 + x = -3.231098884 + 7.8 x = -3.231098884 + 7.8 Combine like terms: -3.231098884 + 7.8 = 4.568901116 x = 4.568901116 Simplifying x = 4.568901116Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.031098884, 4.568901116}
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