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Simplifying 7x(2x) + (3x + -2) = 6x + 50 Remove parenthesis around (2x) 7x * 2x + (3x + -2) = 6x + 50 Reorder the terms for easier multiplication: 7 * 2x * x + (3x + -2) = 6x + 50 Multiply 7 * 2 14x * x + (3x + -2) = 6x + 50 Multiply x * x 14x2 + (3x + -2) = 6x + 50 Reorder the terms: 14x2 + (-2 + 3x) = 6x + 50 Remove parenthesis around (-2 + 3x) 14x2 + -2 + 3x = 6x + 50 Reorder the terms: -2 + 3x + 14x2 = 6x + 50 Reorder the terms: -2 + 3x + 14x2 = 50 + 6x Solving -2 + 3x + 14x2 = 50 + 6x Solving for variable 'x'. Reorder the terms: -2 + -50 + 3x + -6x + 14x2 = 50 + 6x + -50 + -6x Combine like terms: -2 + -50 = -52 -52 + 3x + -6x + 14x2 = 50 + 6x + -50 + -6x Combine like terms: 3x + -6x = -3x -52 + -3x + 14x2 = 50 + 6x + -50 + -6x Reorder the terms: -52 + -3x + 14x2 = 50 + -50 + 6x + -6x Combine like terms: 50 + -50 = 0 -52 + -3x + 14x2 = 0 + 6x + -6x -52 + -3x + 14x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -52 + -3x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -3.714285714 + -0.2142857143x + x2 = 0 Move the constant term to the right: Add '3.714285714' to each side of the equation. -3.714285714 + -0.2142857143x + 3.714285714 + x2 = 0 + 3.714285714 Reorder the terms: -3.714285714 + 3.714285714 + -0.2142857143x + x2 = 0 + 3.714285714 Combine like terms: -3.714285714 + 3.714285714 = 0.000000000 0.000000000 + -0.2142857143x + x2 = 0 + 3.714285714 -0.2142857143x + x2 = 0 + 3.714285714 Combine like terms: 0 + 3.714285714 = 3.714285714 -0.2142857143x + x2 = 3.714285714 The x term is -0.2142857143x. Take half its coefficient (-0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. -0.2142857143x + 0.01147959185 + x2 = 3.714285714 + 0.01147959185 Reorder the terms: 0.01147959185 + -0.2142857143x + x2 = 3.714285714 + 0.01147959185 Combine like terms: 3.714285714 + 0.01147959185 = 3.72576530585 0.01147959185 + -0.2142857143x + x2 = 3.72576530585 Factor a perfect square on the left side: (x + -0.1071428572)(x + -0.1071428572) = 3.72576530585 Calculate the square root of the right side: 1.930224159 Break this problem into two subproblems by setting (x + -0.1071428572) equal to 1.930224159 and -1.930224159.Subproblem 1
x + -0.1071428572 = 1.930224159 Simplifying x + -0.1071428572 = 1.930224159 Reorder the terms: -0.1071428572 + x = 1.930224159 Solving -0.1071428572 + x = 1.930224159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = 1.930224159 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = 1.930224159 + 0.1071428572 x = 1.930224159 + 0.1071428572 Combine like terms: 1.930224159 + 0.1071428572 = 2.0373670162 x = 2.0373670162 Simplifying x = 2.0373670162Subproblem 2
x + -0.1071428572 = -1.930224159 Simplifying x + -0.1071428572 = -1.930224159 Reorder the terms: -0.1071428572 + x = -1.930224159 Solving -0.1071428572 + x = -1.930224159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1071428572' to each side of the equation. -0.1071428572 + 0.1071428572 + x = -1.930224159 + 0.1071428572 Combine like terms: -0.1071428572 + 0.1071428572 = 0.0000000000 0.0000000000 + x = -1.930224159 + 0.1071428572 x = -1.930224159 + 0.1071428572 Combine like terms: -1.930224159 + 0.1071428572 = -1.8230813018 x = -1.8230813018 Simplifying x = -1.8230813018Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0373670162, -1.8230813018}
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