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Simplifying 5.2x(x + -6) = 5 Reorder the terms: 5.2x(-6 + x) = 5 (-6 * 5.2x + x * 5.2x) = 5 (-31.2x + 5.2x2) = 5 Solving -31.2x + 5.2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -31.2x + 5.2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -31.2x + 5.2x2 = 0 Begin completing the square. Divide all terms by 5.2 the coefficient of the squared term: Divide each side by '5.2'. -0.9615384615 + -6x + x2 = 0 Move the constant term to the right: Add '0.9615384615' to each side of the equation. -0.9615384615 + -6x + 0.9615384615 + x2 = 0 + 0.9615384615 Reorder the terms: -0.9615384615 + 0.9615384615 + -6x + x2 = 0 + 0.9615384615 Combine like terms: -0.9615384615 + 0.9615384615 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + 0.9615384615 -6x + x2 = 0 + 0.9615384615 Combine like terms: 0 + 0.9615384615 = 0.9615384615 -6x + x2 = 0.9615384615 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 = 0.9615384615 + 9 Reorder the terms: 9 + -6x + x2 = 0.9615384615 + 9 Combine like terms: 0.9615384615 + 9 = 9.9615384615 9 + -6x + x2 = 9.9615384615 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.9615384615 Calculate the square root of the right side: 3.156190498 Break this problem into two subproblems by setting (x + -3) equal to 3.156190498 and -3.156190498.Subproblem 1
x + -3 = 3.156190498 Simplifying x + -3 = 3.156190498 Reorder the terms: -3 + x = 3.156190498 Solving -3 + x = 3.156190498 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 = 3.156190498 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.156190498 + 3 x = 3.156190498 + 3 Combine like terms: 3.156190498 + 3 = 6.156190498 x = 6.156190498 Simplifying x = 6.156190498Subproblem 2
x + -3 = -3.156190498 Simplifying x + -3 = -3.156190498 Reorder the terms: -3 + x = -3.156190498 Solving -3 + x = -3.156190498 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 = -3.156190498 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.156190498 + 3 x = -3.156190498 + 3 Combine like terms: -3.156190498 + 3 = -0.156190498 x = -0.156190498 Simplifying x = -0.156190498Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.156190498, -0.156190498}
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