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Simplifying 9(x2 + 6x) = 7 Reorder the terms: 9(6x + x2) = 7 (6x * 9 + x2 * 9) = 7 (54x + 9x2) = 7 Solving 54x + 9x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 54x + 9x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + 6x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 6x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 6x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + 0.7777777778 6x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 6x + x2 = 0.7777777778 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 = 0.7777777778 + 9 Reorder the terms: 9 + 6x + x2 = 0.7777777778 + 9 Combine like terms: 0.7777777778 + 9 = 9.7777777778 9 + 6x + x2 = 9.7777777778 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.7777777778 Calculate the square root of the right side: 3.12694384 Break this problem into two subproblems by setting (x + 3) equal to 3.12694384 and -3.12694384.Subproblem 1
x + 3 = 3.12694384 Simplifying x + 3 = 3.12694384 Reorder the terms: 3 + x = 3.12694384 Solving 3 + x = 3.12694384 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 = 3.12694384 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.12694384 + -3 x = 3.12694384 + -3 Combine like terms: 3.12694384 + -3 = 0.12694384 x = 0.12694384 Simplifying x = 0.12694384Subproblem 2
x + 3 = -3.12694384 Simplifying x + 3 = -3.12694384 Reorder the terms: 3 + x = -3.12694384 Solving 3 + x = -3.12694384 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 = -3.12694384 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.12694384 + -3 x = -3.12694384 + -3 Combine like terms: -3.12694384 + -3 = -6.12694384 x = -6.12694384 Simplifying x = -6.12694384Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12694384, -6.12694384}
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