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Simplifying 5x(x + -6) = -6 Reorder the terms: 5x(-6 + x) = -6 (-6 * 5x + x * 5x) = -6 (-30x + 5x2) = -6 Solving -30x + 5x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -30x + 5x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -6x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -6x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -6x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -6x + x2 = 0 + -1.2 -6x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -6x + x2 = -1.2 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 = -1.2 + 9 Reorder the terms: 9 + -6x + x2 = -1.2 + 9 Combine like terms: -1.2 + 9 = 7.8 9 + -6x + x2 = 7.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.8 Calculate the square root of the right side: 2.792848009 Break this problem into two subproblems by setting (x + -3) equal to 2.792848009 and -2.792848009.Subproblem 1
x + -3 = 2.792848009 Simplifying x + -3 = 2.792848009 Reorder the terms: -3 + x = 2.792848009 Solving -3 + x = 2.792848009 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 = 2.792848009 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.792848009 + 3 x = 2.792848009 + 3 Combine like terms: 2.792848009 + 3 = 5.792848009 x = 5.792848009 Simplifying x = 5.792848009Subproblem 2
x + -3 = -2.792848009 Simplifying x + -3 = -2.792848009 Reorder the terms: -3 + x = -2.792848009 Solving -3 + x = -2.792848009 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 = -2.792848009 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.792848009 + 3 x = -2.792848009 + 3 Combine like terms: -2.792848009 + 3 = 0.207151991 x = 0.207151991 Simplifying x = 0.207151991Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.792848009, 0.207151991}
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