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Simplifying 9x2 + 6x = 13 Reorder the terms: 6x + 9x2 = 13 Solving 6x + 9x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 6x + 9x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + 0.6666666667x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + 0.6666666667x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 1.444444444 0.6666666667x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 0.6666666667x + x2 = 1.444444444 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 1.444444444 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.444444444 + 0.1111111112 Combine like terms: 1.444444444 + 0.1111111112 = 1.5555555552 0.1111111112 + 0.6666666667x + x2 = 1.5555555552 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 1.5555555552 Calculate the square root of the right side: 1.247219129 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.247219129 and -1.247219129.Subproblem 1
x + 0.3333333334 = 1.247219129 Simplifying x + 0.3333333334 = 1.247219129 Reorder the terms: 0.3333333334 + x = 1.247219129 Solving 0.3333333334 + x = 1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.247219129 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.247219129 + -0.3333333334 x = 1.247219129 + -0.3333333334 Combine like terms: 1.247219129 + -0.3333333334 = 0.9138857956 x = 0.9138857956 Simplifying x = 0.9138857956Subproblem 2
x + 0.3333333334 = -1.247219129 Simplifying x + 0.3333333334 = -1.247219129 Reorder the terms: 0.3333333334 + x = -1.247219129 Solving 0.3333333334 + x = -1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.247219129 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.247219129 + -0.3333333334 x = -1.247219129 + -0.3333333334 Combine like terms: -1.247219129 + -0.3333333334 = -1.5805524624 x = -1.5805524624 Simplifying x = -1.5805524624Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9138857956, -1.5805524624}
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