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Simplifying 0 = -0.6x2 + 6x + -5 Reorder the terms: 0 = -5 + 6x + -0.6x2 Solving 0 = -5 + 6x + -0.6x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + -6x + 0.6x2 = -5 + 6x + -0.6x2 + 5 + -6x + 0.6x2 Reorder the terms: 5 + -6x + 0.6x2 = -5 + 5 + 6x + -6x + -0.6x2 + 0.6x2 Combine like terms: -5 + 5 = 0 5 + -6x + 0.6x2 = 0 + 6x + -6x + -0.6x2 + 0.6x2 5 + -6x + 0.6x2 = 6x + -6x + -0.6x2 + 0.6x2 Combine like terms: 6x + -6x = 0 5 + -6x + 0.6x2 = 0 + -0.6x2 + 0.6x2 5 + -6x + 0.6x2 = -0.6x2 + 0.6x2 Combine like terms: -0.6x2 + 0.6x2 = 0.0 5 + -6x + 0.6x2 = 0.0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 8.333333333 + -10x + x2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -10x + -8.333333333 + x2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -10x + x2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -10x + x2 = 0 + -8.333333333 -10x + x2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -10x + x2 = -8.333333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -8.333333333 + 25 Reorder the terms: 25 + -10x + x2 = -8.333333333 + 25 Combine like terms: -8.333333333 + 25 = 16.666666667 25 + -10x + x2 = 16.666666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 16.666666667 Calculate the square root of the right side: 4.082482905 Break this problem into two subproblems by setting (x + -5) equal to 4.082482905 and -4.082482905.Subproblem 1
x + -5 = 4.082482905 Simplifying x + -5 = 4.082482905 Reorder the terms: -5 + x = 4.082482905 Solving -5 + x = 4.082482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.082482905 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.082482905 + 5 x = 4.082482905 + 5 Combine like terms: 4.082482905 + 5 = 9.082482905 x = 9.082482905 Simplifying x = 9.082482905Subproblem 2
x + -5 = -4.082482905 Simplifying x + -5 = -4.082482905 Reorder the terms: -5 + x = -4.082482905 Solving -5 + x = -4.082482905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.082482905 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.082482905 + 5 x = -4.082482905 + 5 Combine like terms: -4.082482905 + 5 = 0.917517095 x = 0.917517095 Simplifying x = 0.917517095Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.082482905, 0.917517095}
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