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Simplifying 9x2 + 6x + -100 = 0 Reorder the terms: -100 + 6x + 9x2 = 0 Solving -100 + 6x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -11.11111111 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + 0.6666666667x + 11.11111111 + x2 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + 0.6666666667x + x2 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + 0.6666666667x + x2 = 0 + 11.11111111 0.6666666667x + x2 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 0.6666666667x + x2 = 11.11111111 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 = 11.11111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 11.11111111 + 0.1111111112 Combine like terms: 11.11111111 + 0.1111111112 = 11.2222222212 0.1111111112 + 0.6666666667x + x2 = 11.2222222212 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 11.2222222212 Calculate the square root of the right side: 3.34995854 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 3.34995854 and -3.34995854.Subproblem 1
x + 0.3333333334 = 3.34995854 Simplifying x + 0.3333333334 = 3.34995854 Reorder the terms: 0.3333333334 + x = 3.34995854 Solving 0.3333333334 + x = 3.34995854 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 = 3.34995854 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.34995854 + -0.3333333334 x = 3.34995854 + -0.3333333334 Combine like terms: 3.34995854 + -0.3333333334 = 3.0166252066 x = 3.0166252066 Simplifying x = 3.0166252066Subproblem 2
x + 0.3333333334 = -3.34995854 Simplifying x + 0.3333333334 = -3.34995854 Reorder the terms: 0.3333333334 + x = -3.34995854 Solving 0.3333333334 + x = -3.34995854 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 = -3.34995854 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.34995854 + -0.3333333334 x = -3.34995854 + -0.3333333334 Combine like terms: -3.34995854 + -0.3333333334 = -3.6832918734 x = -3.6832918734 Simplifying x = -3.6832918734Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0166252066, -3.6832918734}
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