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Simplifying 7x2 = 3x + 11 Reorder the terms: 7x2 = 11 + 3x Solving 7x2 = 11 + 3x Solving for variable 'x'. Reorder the terms: -11 + -3x + 7x2 = 11 + 3x + -11 + -3x Reorder the terms: -11 + -3x + 7x2 = 11 + -11 + 3x + -3x Combine like terms: 11 + -11 = 0 -11 + -3x + 7x2 = 0 + 3x + -3x -11 + -3x + 7x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -11 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -0.4285714286x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -0.4285714286x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 1.571428571 -0.4285714286x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -0.4285714286x + x2 = 1.571428571 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 = 1.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 1.571428571 + 0.04591836735 Combine like terms: 1.571428571 + 0.04591836735 = 1.61734693835 0.04591836735 + -0.4285714286x + x2 = 1.61734693835 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 1.61734693835 Calculate the square root of the right side: 1.271749558 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 1.271749558 and -1.271749558.Subproblem 1
x + -0.2142857143 = 1.271749558 Simplifying x + -0.2142857143 = 1.271749558 Reorder the terms: -0.2142857143 + x = 1.271749558 Solving -0.2142857143 + x = 1.271749558 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 = 1.271749558 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 1.271749558 + 0.2142857143 x = 1.271749558 + 0.2142857143 Combine like terms: 1.271749558 + 0.2142857143 = 1.4860352723 x = 1.4860352723 Simplifying x = 1.4860352723Subproblem 2
x + -0.2142857143 = -1.271749558 Simplifying x + -0.2142857143 = -1.271749558 Reorder the terms: -0.2142857143 + x = -1.271749558 Solving -0.2142857143 + x = -1.271749558 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 = -1.271749558 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -1.271749558 + 0.2142857143 x = -1.271749558 + 0.2142857143 Combine like terms: -1.271749558 + 0.2142857143 = -1.0574638437 x = -1.0574638437 Simplifying x = -1.0574638437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4860352723, -1.0574638437}
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