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Simplifying 7x2 + 3x = 12 Reorder the terms: 3x + 7x2 = 12 Solving 3x + 7x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 3x + 7x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + 0.4285714286x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + 0.4285714286x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 1.714285714 0.4285714286x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 0.4285714286x + x2 = 1.714285714 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 = 1.714285714 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1.714285714 + 0.04591836735 Combine like terms: 1.714285714 + 0.04591836735 = 1.76020408135 0.04591836735 + 0.4285714286x + x2 = 1.76020408135 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.76020408135 Calculate the square root of the right side: 1.32672683 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.32672683 and -1.32672683.Subproblem 1
x + 0.2142857143 = 1.32672683 Simplifying x + 0.2142857143 = 1.32672683 Reorder the terms: 0.2142857143 + x = 1.32672683 Solving 0.2142857143 + x = 1.32672683 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 = 1.32672683 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.32672683 + -0.2142857143 x = 1.32672683 + -0.2142857143 Combine like terms: 1.32672683 + -0.2142857143 = 1.1124411157 x = 1.1124411157 Simplifying x = 1.1124411157Subproblem 2
x + 0.2142857143 = -1.32672683 Simplifying x + 0.2142857143 = -1.32672683 Reorder the terms: 0.2142857143 + x = -1.32672683 Solving 0.2142857143 + x = -1.32672683 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 = -1.32672683 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.32672683 + -0.2142857143 x = -1.32672683 + -0.2142857143 Combine like terms: -1.32672683 + -0.2142857143 = -1.5410125443 x = -1.5410125443 Simplifying x = -1.5410125443Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1124411157, -1.5410125443}
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