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Simplifying 9x2 + 6x + -19 = 0 Reorder the terms: -19 + 6x + 9x2 = 0 Solving -19 + 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'. -2.111111111 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '2.111111111' to each side of the equation. -2.111111111 + 0.6666666667x + 2.111111111 + x2 = 0 + 2.111111111 Reorder the terms: -2.111111111 + 2.111111111 + 0.6666666667x + x2 = 0 + 2.111111111 Combine like terms: -2.111111111 + 2.111111111 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + 2.111111111 0.6666666667x + x2 = 0 + 2.111111111 Combine like terms: 0 + 2.111111111 = 2.111111111 0.6666666667x + x2 = 2.111111111 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 = 2.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 2.111111111 + 0.1111111112 Combine like terms: 2.111111111 + 0.1111111112 = 2.2222222222 0.1111111112 + 0.6666666667x + x2 = 2.2222222222 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.2222222222 Calculate the square root of the right side: 1.490711985 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.490711985 and -1.490711985.Subproblem 1
x + 0.3333333334 = 1.490711985 Simplifying x + 0.3333333334 = 1.490711985 Reorder the terms: 0.3333333334 + x = 1.490711985 Solving 0.3333333334 + x = 1.490711985 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 = 1.490711985 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.490711985 + -0.3333333334 x = 1.490711985 + -0.3333333334 Combine like terms: 1.490711985 + -0.3333333334 = 1.1573786516 x = 1.1573786516 Simplifying x = 1.1573786516Subproblem 2
x + 0.3333333334 = -1.490711985 Simplifying x + 0.3333333334 = -1.490711985 Reorder the terms: 0.3333333334 + x = -1.490711985 Solving 0.3333333334 + x = -1.490711985 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 = -1.490711985 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.490711985 + -0.3333333334 x = -1.490711985 + -0.3333333334 Combine like terms: -1.490711985 + -0.3333333334 = -1.8240453184 x = -1.8240453184 Simplifying x = -1.8240453184Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1573786516, -1.8240453184}
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