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Simplifying 9x2 + 6x + -10 = 0 Reorder the terms: -10 + 6x + 9x2 = 0 Solving -10 + 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'. -1.111111111 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 0.6666666667x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 0.6666666667x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 1.111111111 0.6666666667x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 0.6666666667x + x2 = 1.111111111 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 = 1.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 1.111111111 + 0.1111111112 Combine like terms: 1.111111111 + 0.1111111112 = 1.2222222222 0.1111111112 + 0.6666666667x + x2 = 1.2222222222 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 1.2222222222 Calculate the square root of the right side: 1.105541597 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.105541597 and -1.105541597.Subproblem 1
x + 0.3333333334 = 1.105541597 Simplifying x + 0.3333333334 = 1.105541597 Reorder the terms: 0.3333333334 + x = 1.105541597 Solving 0.3333333334 + x = 1.105541597 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 = 1.105541597 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.105541597 + -0.3333333334 x = 1.105541597 + -0.3333333334 Combine like terms: 1.105541597 + -0.3333333334 = 0.7722082636 x = 0.7722082636 Simplifying x = 0.7722082636Subproblem 2
x + 0.3333333334 = -1.105541597 Simplifying x + 0.3333333334 = -1.105541597 Reorder the terms: 0.3333333334 + x = -1.105541597 Solving 0.3333333334 + x = -1.105541597 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 = -1.105541597 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.105541597 + -0.3333333334 x = -1.105541597 + -0.3333333334 Combine like terms: -1.105541597 + -0.3333333334 = -1.4388749304 x = -1.4388749304 Simplifying x = -1.4388749304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7722082636, -1.4388749304}
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