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Simplifying 7x2 + 15x + -14 = 0 Reorder the terms: -14 + 15x + 7x2 = 0 Solving -14 + 15x + 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'. -2 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.142857143x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.142857143x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.142857143x + x2 = 0 + 2 2.142857143x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.142857143x + x2 = 2 The x term is 2.142857143x. Take half its coefficient (1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. 2.142857143x + 1.147959185 + x2 = 2 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 2 + 1.147959185 Combine like terms: 2 + 1.147959185 = 3.147959185 1.147959185 + 2.142857143x + x2 = 3.147959185 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 3.147959185 Calculate the square root of the right side: 1.774248907 Break this problem into two subproblems by setting (x + 1.071428572) equal to 1.774248907 and -1.774248907.Subproblem 1
x + 1.071428572 = 1.774248907 Simplifying x + 1.071428572 = 1.774248907 Reorder the terms: 1.071428572 + x = 1.774248907 Solving 1.071428572 + x = 1.774248907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 1.774248907 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 1.774248907 + -1.071428572 x = 1.774248907 + -1.071428572 Combine like terms: 1.774248907 + -1.071428572 = 0.702820335 x = 0.702820335 Simplifying x = 0.702820335Subproblem 2
x + 1.071428572 = -1.774248907 Simplifying x + 1.071428572 = -1.774248907 Reorder the terms: 1.071428572 + x = -1.774248907 Solving 1.071428572 + x = -1.774248907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -1.774248907 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -1.774248907 + -1.071428572 x = -1.774248907 + -1.071428572 Combine like terms: -1.774248907 + -1.071428572 = -2.845677479 x = -2.845677479 Simplifying x = -2.845677479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.702820335, -2.845677479}
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