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Simplifying (7x2 + 6x + -7) + -1(5x + 14) = 0 Reorder the terms: (-7 + 6x + 7x2) + -1(5x + 14) = 0 Remove parenthesis around (-7 + 6x + 7x2) -7 + 6x + 7x2 + -1(5x + 14) = 0 Reorder the terms: -7 + 6x + 7x2 + -1(14 + 5x) = 0 -7 + 6x + 7x2 + (14 * -1 + 5x * -1) = 0 -7 + 6x + 7x2 + (-14 + -5x) = 0 Reorder the terms: -7 + -14 + 6x + -5x + 7x2 = 0 Combine like terms: -7 + -14 = -21 -21 + 6x + -5x + 7x2 = 0 Combine like terms: 6x + -5x = 1x -21 + 1x + 7x2 = 0 Solving -21 + 1x + 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'. -3 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.1428571429x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.1428571429x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.1428571429x + x2 = 0 + 3 0.1428571429x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.1428571429x + x2 = 3 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 3 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 3 + 0.005102040819 Combine like terms: 3 + 0.005102040819 = 3.005102040819 0.005102040819 + 0.1428571429x + x2 = 3.005102040819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 3.005102040819 Calculate the square root of the right side: 1.733523014 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 1.733523014 and -1.733523014.Subproblem 1
x + 0.07142857145 = 1.733523014 Simplifying x + 0.07142857145 = 1.733523014 Reorder the terms: 0.07142857145 + x = 1.733523014 Solving 0.07142857145 + x = 1.733523014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 1.733523014 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 1.733523014 + -0.07142857145 x = 1.733523014 + -0.07142857145 Combine like terms: 1.733523014 + -0.07142857145 = 1.66209444255 x = 1.66209444255 Simplifying x = 1.66209444255Subproblem 2
x + 0.07142857145 = -1.733523014 Simplifying x + 0.07142857145 = -1.733523014 Reorder the terms: 0.07142857145 + x = -1.733523014 Solving 0.07142857145 + x = -1.733523014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -1.733523014 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -1.733523014 + -0.07142857145 x = -1.733523014 + -0.07142857145 Combine like terms: -1.733523014 + -0.07142857145 = -1.80495158545 x = -1.80495158545 Simplifying x = -1.80495158545Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.66209444255, -1.80495158545}
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