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Simplifying x + 5x(6x + -3) = 165 Reorder the terms: x + 5x(-3 + 6x) = 165 x + (-3 * 5x + 6x * 5x) = 165 x + (-15x + 30x2) = 165 Combine like terms: x + -15x = -14x -14x + 30x2 = 165 Solving -14x + 30x2 = 165 Solving for variable 'x'. Reorder the terms: -165 + -14x + 30x2 = 165 + -165 Combine like terms: 165 + -165 = 0 -165 + -14x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -5.5 + -0.4666666667x + x2 = 0.0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -0.4666666667x + 5.5 + x2 = 0.0 + 5.5 Reorder the terms: -5.5 + 5.5 + -0.4666666667x + x2 = 0.0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -0.4666666667x + x2 = 0.0 + 5.5 -0.4666666667x + x2 = 0.0 + 5.5 Combine like terms: 0.0 + 5.5 = 5.5 -0.4666666667x + x2 = 5.5 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = 5.5 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = 5.5 + 0.05444444448 Combine like terms: 5.5 + 0.05444444448 = 5.55444444448 0.05444444448 + -0.4666666667x + x2 = 5.55444444448 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = 5.55444444448 Calculate the square root of the right side: 2.35678689 Break this problem into two subproblems by setting (x + -0.2333333334) equal to 2.35678689 and -2.35678689.Subproblem 1
x + -0.2333333334 = 2.35678689 Simplifying x + -0.2333333334 = 2.35678689 Reorder the terms: -0.2333333334 + x = 2.35678689 Solving -0.2333333334 + x = 2.35678689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = 2.35678689 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = 2.35678689 + 0.2333333334 x = 2.35678689 + 0.2333333334 Combine like terms: 2.35678689 + 0.2333333334 = 2.5901202234 x = 2.5901202234 Simplifying x = 2.5901202234Subproblem 2
x + -0.2333333334 = -2.35678689 Simplifying x + -0.2333333334 = -2.35678689 Reorder the terms: -0.2333333334 + x = -2.35678689 Solving -0.2333333334 + x = -2.35678689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2333333334' to each side of the equation. -0.2333333334 + 0.2333333334 + x = -2.35678689 + 0.2333333334 Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000 0.0000000000 + x = -2.35678689 + 0.2333333334 x = -2.35678689 + 0.2333333334 Combine like terms: -2.35678689 + 0.2333333334 = -2.1234535566 x = -2.1234535566 Simplifying x = -2.1234535566Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5901202234, -2.1234535566}
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