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Simplifying 16 + -56x + 49x2 = 78 Solving 16 + -56x + 49x2 = 78 Solving for variable 'x'. Reorder the terms: 16 + -78 + -56x + 49x2 = 78 + -78 Combine like terms: 16 + -78 = -62 -62 + -56x + 49x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -62 + -56x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.265306122 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '1.265306122' to each side of the equation. -1.265306122 + -1.142857143x + 1.265306122 + x2 = 0 + 1.265306122 Reorder the terms: -1.265306122 + 1.265306122 + -1.142857143x + x2 = 0 + 1.265306122 Combine like terms: -1.265306122 + 1.265306122 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 1.265306122 -1.142857143x + x2 = 0 + 1.265306122 Combine like terms: 0 + 1.265306122 = 1.265306122 -1.142857143x + x2 = 1.265306122 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 1.265306122 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 1.265306122 + 0.3265306123 Combine like terms: 1.265306122 + 0.3265306123 = 1.5918367343 0.3265306123 + -1.142857143x + x2 = 1.5918367343 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.5918367343 Calculate the square root of the right side: 1.261680124 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.261680124 and -1.261680124.Subproblem 1
x + -0.5714285715 = 1.261680124 Simplifying x + -0.5714285715 = 1.261680124 Reorder the terms: -0.5714285715 + x = 1.261680124 Solving -0.5714285715 + x = 1.261680124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 1.261680124 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.261680124 + 0.5714285715 x = 1.261680124 + 0.5714285715 Combine like terms: 1.261680124 + 0.5714285715 = 1.8331086955 x = 1.8331086955 Simplifying x = 1.8331086955Subproblem 2
x + -0.5714285715 = -1.261680124 Simplifying x + -0.5714285715 = -1.261680124 Reorder the terms: -0.5714285715 + x = -1.261680124 Solving -0.5714285715 + x = -1.261680124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -1.261680124 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.261680124 + 0.5714285715 x = -1.261680124 + 0.5714285715 Combine like terms: -1.261680124 + 0.5714285715 = -0.6902515525 x = -0.6902515525 Simplifying x = -0.6902515525Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8331086955, -0.6902515525}
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