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Simplifying (3x2 + -4x + 12) + (4x2 + 7x + -86) = 0 Reorder the terms: (12 + -4x + 3x2) + (4x2 + 7x + -86) = 0 Remove parenthesis around (12 + -4x + 3x2) 12 + -4x + 3x2 + (4x2 + 7x + -86) = 0 Reorder the terms: 12 + -4x + 3x2 + (-86 + 7x + 4x2) = 0 Remove parenthesis around (-86 + 7x + 4x2) 12 + -4x + 3x2 + -86 + 7x + 4x2 = 0 Reorder the terms: 12 + -86 + -4x + 7x + 3x2 + 4x2 = 0 Combine like terms: 12 + -86 = -74 -74 + -4x + 7x + 3x2 + 4x2 = 0 Combine like terms: -4x + 7x = 3x -74 + 3x + 3x2 + 4x2 = 0 Combine like terms: 3x2 + 4x2 = 7x2 -74 + 3x + 7x2 = 0 Solving -74 + 3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -10.57142857 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '10.57142857' to each side of the equation. -10.57142857 + 0.4285714286x + 10.57142857 + x2 = 0 + 10.57142857 Reorder the terms: -10.57142857 + 10.57142857 + 0.4285714286x + x2 = 0 + 10.57142857 Combine like terms: -10.57142857 + 10.57142857 = 0.00000000 0.00000000 + 0.4285714286x + x2 = 0 + 10.57142857 0.4285714286x + x2 = 0 + 10.57142857 Combine like terms: 0 + 10.57142857 = 10.57142857 0.4285714286x + x2 = 10.57142857 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 10.57142857 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 10.57142857 + 0.04591836735 Combine like terms: 10.57142857 + 0.04591836735 = 10.61734693735 0.04591836735 + 0.4285714286x + x2 = 10.61734693735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 10.61734693735 Calculate the square root of the right side: 3.258427065 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 3.258427065 and -3.258427065.Subproblem 1
x + 0.2142857143 = 3.258427065 Simplifying x + 0.2142857143 = 3.258427065 Reorder the terms: 0.2142857143 + x = 3.258427065 Solving 0.2142857143 + x = 3.258427065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 3.258427065 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 3.258427065 + -0.2142857143 x = 3.258427065 + -0.2142857143 Combine like terms: 3.258427065 + -0.2142857143 = 3.0441413507 x = 3.0441413507 Simplifying x = 3.0441413507Subproblem 2
x + 0.2142857143 = -3.258427065 Simplifying x + 0.2142857143 = -3.258427065 Reorder the terms: 0.2142857143 + x = -3.258427065 Solving 0.2142857143 + x = -3.258427065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -3.258427065 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -3.258427065 + -0.2142857143 x = -3.258427065 + -0.2142857143 Combine like terms: -3.258427065 + -0.2142857143 = -3.4727127793 x = -3.4727127793 Simplifying x = -3.4727127793Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0441413507, -3.4727127793}
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