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Simplifying 345x * x + -6788x = 678 Multiply x * x 345x2 + -6788x = 678 Reorder the terms: -6788x + 345x2 = 678 Solving -6788x + 345x2 = 678 Solving for variable 'x'. Reorder the terms: -678 + -6788x + 345x2 = 678 + -678 Combine like terms: 678 + -678 = 0 -678 + -6788x + 345x2 = 0 Begin completing the square. Divide all terms by 345 the coefficient of the squared term: Divide each side by '345'. -1.965217391 + -19.67536232x + x2 = 0 Move the constant term to the right: Add '1.965217391' to each side of the equation. -1.965217391 + -19.67536232x + 1.965217391 + x2 = 0 + 1.965217391 Reorder the terms: -1.965217391 + 1.965217391 + -19.67536232x + x2 = 0 + 1.965217391 Combine like terms: -1.965217391 + 1.965217391 = 0.000000000 0.000000000 + -19.67536232x + x2 = 0 + 1.965217391 -19.67536232x + x2 = 0 + 1.965217391 Combine like terms: 0 + 1.965217391 = 1.965217391 -19.67536232x + x2 = 1.965217391 The x term is -19.67536232x. Take half its coefficient (-9.83768116). Square it (96.77997061) and add it to both sides. Add '96.77997061' to each side of the equation. -19.67536232x + 96.77997061 + x2 = 1.965217391 + 96.77997061 Reorder the terms: 96.77997061 + -19.67536232x + x2 = 1.965217391 + 96.77997061 Combine like terms: 1.965217391 + 96.77997061 = 98.745188001 96.77997061 + -19.67536232x + x2 = 98.745188001 Factor a perfect square on the left side: (x + -9.83768116)(x + -9.83768116) = 98.745188001 Calculate the square root of the right side: 9.937061336 Break this problem into two subproblems by setting (x + -9.83768116) equal to 9.937061336 and -9.937061336.Subproblem 1
x + -9.83768116 = 9.937061336 Simplifying x + -9.83768116 = 9.937061336 Reorder the terms: -9.83768116 + x = 9.937061336 Solving -9.83768116 + x = 9.937061336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.83768116' to each side of the equation. -9.83768116 + 9.83768116 + x = 9.937061336 + 9.83768116 Combine like terms: -9.83768116 + 9.83768116 = 0.00000000 0.00000000 + x = 9.937061336 + 9.83768116 x = 9.937061336 + 9.83768116 Combine like terms: 9.937061336 + 9.83768116 = 19.774742496 x = 19.774742496 Simplifying x = 19.774742496Subproblem 2
x + -9.83768116 = -9.937061336 Simplifying x + -9.83768116 = -9.937061336 Reorder the terms: -9.83768116 + x = -9.937061336 Solving -9.83768116 + x = -9.937061336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.83768116' to each side of the equation. -9.83768116 + 9.83768116 + x = -9.937061336 + 9.83768116 Combine like terms: -9.83768116 + 9.83768116 = 0.00000000 0.00000000 + x = -9.937061336 + 9.83768116 x = -9.937061336 + 9.83768116 Combine like terms: -9.937061336 + 9.83768116 = -0.099380176 x = -0.099380176 Simplifying x = -0.099380176Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.774742496, -0.099380176}
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