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Simplifying 7x2 + 42x + -2 = 0 Reorder the terms: -2 + 42x + 7x2 = 0 Solving -2 + 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'. -0.2857142857 + 6x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 6x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 6x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + 0.2857142857 6x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 6x + x2 = 0.2857142857 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 = 0.2857142857 + 9 Reorder the terms: 9 + 6x + x2 = 0.2857142857 + 9 Combine like terms: 0.2857142857 + 9 = 9.2857142857 9 + 6x + x2 = 9.2857142857 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.2857142857 Calculate the square root of the right side: 3.047247001 Break this problem into two subproblems by setting (x + 3) equal to 3.047247001 and -3.047247001.Subproblem 1
x + 3 = 3.047247001 Simplifying x + 3 = 3.047247001 Reorder the terms: 3 + x = 3.047247001 Solving 3 + x = 3.047247001 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 = 3.047247001 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.047247001 + -3 x = 3.047247001 + -3 Combine like terms: 3.047247001 + -3 = 0.047247001 x = 0.047247001 Simplifying x = 0.047247001Subproblem 2
x + 3 = -3.047247001 Simplifying x + 3 = -3.047247001 Reorder the terms: 3 + x = -3.047247001 Solving 3 + x = -3.047247001 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 = -3.047247001 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.047247001 + -3 x = -3.047247001 + -3 Combine like terms: -3.047247001 + -3 = -6.047247001 x = -6.047247001 Simplifying x = -6.047247001Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047247001, -6.047247001}
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