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Simplifying 5x(x + -6) = 27 Reorder the terms: 5x(-6 + x) = 27 (-6 * 5x + x * 5x) = 27 (-30x + 5x2) = 27 Solving -30x + 5x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -30x + 5x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -6x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -6x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -6x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -6x + x2 = 0 + 5.4 -6x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -6x + x2 = 5.4 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5.4 + 9 Reorder the terms: 9 + -6x + x2 = 5.4 + 9 Combine like terms: 5.4 + 9 = 14.4 9 + -6x + x2 = 14.4 Factor a perfect square on the left side: (x + -3)(x + -3) = 14.4 Calculate the square root of the right side: 3.794733192 Break this problem into two subproblems by setting (x + -3) equal to 3.794733192 and -3.794733192.Subproblem 1
x + -3 = 3.794733192 Simplifying x + -3 = 3.794733192 Reorder the terms: -3 + x = 3.794733192 Solving -3 + x = 3.794733192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.794733192 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.794733192 + 3 x = 3.794733192 + 3 Combine like terms: 3.794733192 + 3 = 6.794733192 x = 6.794733192 Simplifying x = 6.794733192Subproblem 2
x + -3 = -3.794733192 Simplifying x + -3 = -3.794733192 Reorder the terms: -3 + x = -3.794733192 Solving -3 + x = -3.794733192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.794733192 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.794733192 + 3 x = -3.794733192 + 3 Combine like terms: -3.794733192 + 3 = -0.794733192 x = -0.794733192 Simplifying x = -0.794733192Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.794733192, -0.794733192}
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