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Simplifying 7x2 + 42x + 45 = 0 Reorder the terms: 45 + 42x + 7x2 = 0 Solving 45 + 42x + 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'. 6.428571429 + 6x + x2 = 0 Move the constant term to the right: Add '-6.428571429' to each side of the equation. 6.428571429 + 6x + -6.428571429 + x2 = 0 + -6.428571429 Reorder the terms: 6.428571429 + -6.428571429 + 6x + x2 = 0 + -6.428571429 Combine like terms: 6.428571429 + -6.428571429 = 0.000000000 0.000000000 + 6x + x2 = 0 + -6.428571429 6x + x2 = 0 + -6.428571429 Combine like terms: 0 + -6.428571429 = -6.428571429 6x + x2 = -6.428571429 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -6.428571429 + 9 Reorder the terms: 9 + 6x + x2 = -6.428571429 + 9 Combine like terms: -6.428571429 + 9 = 2.571428571 9 + 6x + x2 = 2.571428571 Factor a perfect square on the left side: (x + 3)(x + 3) = 2.571428571 Calculate the square root of the right side: 1.603567451 Break this problem into two subproblems by setting (x + 3) equal to 1.603567451 and -1.603567451.Subproblem 1
x + 3 = 1.603567451 Simplifying x + 3 = 1.603567451 Reorder the terms: 3 + x = 1.603567451 Solving 3 + x = 1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.603567451 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.603567451 + -3 x = 1.603567451 + -3 Combine like terms: 1.603567451 + -3 = -1.396432549 x = -1.396432549 Simplifying x = -1.396432549Subproblem 2
x + 3 = -1.603567451 Simplifying x + 3 = -1.603567451 Reorder the terms: 3 + x = -1.603567451 Solving 3 + x = -1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.603567451 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.603567451 + -3 x = -1.603567451 + -3 Combine like terms: -1.603567451 + -3 = -4.603567451 x = -4.603567451 Simplifying x = -4.603567451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.396432549, -4.603567451}
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