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Simplifying 7x2 + 3x + -12 = 6 Reorder the terms: -12 + 3x + 7x2 = 6 Solving -12 + 3x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: -12 + -6 + 3x + 7x2 = 6 + -6 Combine like terms: -12 + -6 = -18 -18 + 3x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -18 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + 0.4285714286x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + 0.4285714286x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 2.571428571 0.4285714286x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 0.4285714286x + x2 = 2.571428571 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 = 2.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 2.571428571 + 0.04591836735 Combine like terms: 2.571428571 + 0.04591836735 = 2.61734693835 0.04591836735 + 0.4285714286x + x2 = 2.61734693835 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 2.61734693835 Calculate the square root of the right side: 1.617821665 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.617821665 and -1.617821665.Subproblem 1
x + 0.2142857143 = 1.617821665 Simplifying x + 0.2142857143 = 1.617821665 Reorder the terms: 0.2142857143 + x = 1.617821665 Solving 0.2142857143 + x = 1.617821665 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 = 1.617821665 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.617821665 + -0.2142857143 x = 1.617821665 + -0.2142857143 Combine like terms: 1.617821665 + -0.2142857143 = 1.4035359507 x = 1.4035359507 Simplifying x = 1.4035359507Subproblem 2
x + 0.2142857143 = -1.617821665 Simplifying x + 0.2142857143 = -1.617821665 Reorder the terms: 0.2142857143 + x = -1.617821665 Solving 0.2142857143 + x = -1.617821665 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 = -1.617821665 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.617821665 + -0.2142857143 x = -1.617821665 + -0.2142857143 Combine like terms: -1.617821665 + -0.2142857143 = -1.8321073793 x = -1.8321073793 Simplifying x = -1.8321073793Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4035359507, -1.8321073793}
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