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Simplifying 7x2 + 15x + -35 = 0 Reorder the terms: -35 + 15x + 7x2 = 0 Solving -35 + 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'. -5 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.142857143x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.142857143x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.142857143x + x2 = 0 + 5 2.142857143x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.142857143x + x2 = 5 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 = 5 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 5 + 1.147959185 Combine like terms: 5 + 1.147959185 = 6.147959185 1.147959185 + 2.142857143x + x2 = 6.147959185 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 6.147959185 Calculate the square root of the right side: 2.479507851 Break this problem into two subproblems by setting (x + 1.071428572) equal to 2.479507851 and -2.479507851.Subproblem 1
x + 1.071428572 = 2.479507851 Simplifying x + 1.071428572 = 2.479507851 Reorder the terms: 1.071428572 + x = 2.479507851 Solving 1.071428572 + x = 2.479507851 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 = 2.479507851 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 2.479507851 + -1.071428572 x = 2.479507851 + -1.071428572 Combine like terms: 2.479507851 + -1.071428572 = 1.408079279 x = 1.408079279 Simplifying x = 1.408079279Subproblem 2
x + 1.071428572 = -2.479507851 Simplifying x + 1.071428572 = -2.479507851 Reorder the terms: 1.071428572 + x = -2.479507851 Solving 1.071428572 + x = -2.479507851 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 = -2.479507851 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -2.479507851 + -1.071428572 x = -2.479507851 + -1.071428572 Combine like terms: -2.479507851 + -1.071428572 = -3.550936423 x = -3.550936423 Simplifying x = -3.550936423Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.408079279, -3.550936423}
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