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Simplifying 3x2 + -78x + 56 = 0 Reorder the terms: 56 + -78x + 3x2 = 0 Solving 56 + -78x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 18.66666667 + -26x + x2 = 0 Move the constant term to the right: Add '-18.66666667' to each side of the equation. 18.66666667 + -26x + -18.66666667 + x2 = 0 + -18.66666667 Reorder the terms: 18.66666667 + -18.66666667 + -26x + x2 = 0 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + -26x + x2 = 0 + -18.66666667 -26x + x2 = 0 + -18.66666667 Combine like terms: 0 + -18.66666667 = -18.66666667 -26x + x2 = -18.66666667 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -18.66666667 + 169 Reorder the terms: 169 + -26x + x2 = -18.66666667 + 169 Combine like terms: -18.66666667 + 169 = 150.33333333 169 + -26x + x2 = 150.33333333 Factor a perfect square on the left side: (x + -13)(x + -13) = 150.33333333 Calculate the square root of the right side: 12.261049438 Break this problem into two subproblems by setting (x + -13) equal to 12.261049438 and -12.261049438.Subproblem 1
x + -13 = 12.261049438 Simplifying x + -13 = 12.261049438 Reorder the terms: -13 + x = 12.261049438 Solving -13 + x = 12.261049438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.261049438 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.261049438 + 13 x = 12.261049438 + 13 Combine like terms: 12.261049438 + 13 = 25.261049438 x = 25.261049438 Simplifying x = 25.261049438Subproblem 2
x + -13 = -12.261049438 Simplifying x + -13 = -12.261049438 Reorder the terms: -13 + x = -12.261049438 Solving -13 + x = -12.261049438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.261049438 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.261049438 + 13 x = -12.261049438 + 13 Combine like terms: -12.261049438 + 13 = 0.738950562 x = 0.738950562 Simplifying x = 0.738950562Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.261049438, 0.738950562}
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