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Simplifying 10 + 4 = 5x(x + -6) Combine like terms: 10 + 4 = 14 14 = 5x(x + -6) Reorder the terms: 14 = 5x(-6 + x) 14 = (-6 * 5x + x * 5x) 14 = (-30x + 5x2) Solving 14 = -30x + 5x2 Solving for variable 'x'. Reorder the terms: 14 + 30x + -5x2 = -30x + 30x + 5x2 + -5x2 Combine like terms: -30x + 30x = 0 14 + 30x + -5x2 = 0 + 5x2 + -5x2 14 + 30x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 14 + 30x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.8 + -6x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -6x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -6x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -6x + x2 = 0 + 2.8 -6x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -6x + x2 = 2.8 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 = 2.8 + 9 Reorder the terms: 9 + -6x + x2 = 2.8 + 9 Combine like terms: 2.8 + 9 = 11.8 9 + -6x + x2 = 11.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 11.8 Calculate the square root of the right side: 3.435112807 Break this problem into two subproblems by setting (x + -3) equal to 3.435112807 and -3.435112807.Subproblem 1
x + -3 = 3.435112807 Simplifying x + -3 = 3.435112807 Reorder the terms: -3 + x = 3.435112807 Solving -3 + x = 3.435112807 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 = 3.435112807 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.435112807 + 3 x = 3.435112807 + 3 Combine like terms: 3.435112807 + 3 = 6.435112807 x = 6.435112807 Simplifying x = 6.435112807Subproblem 2
x + -3 = -3.435112807 Simplifying x + -3 = -3.435112807 Reorder the terms: -3 + x = -3.435112807 Solving -3 + x = -3.435112807 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 = -3.435112807 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.435112807 + 3 x = -3.435112807 + 3 Combine like terms: -3.435112807 + 3 = -0.435112807 x = -0.435112807 Simplifying x = -0.435112807Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.435112807, -0.435112807}
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