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Simplifying 3 = 0.6x2 + -1x + -7 Reorder the terms: 3 = -7 + -1x + 0.6x2 Solving 3 = -7 + -1x + 0.6x2 Solving for variable 'x'. Combine like terms: 3 + 7 = 10 10 + x + -0.6x2 = -7 + -1x + 0.6x2 + 7 + x + -0.6x2 Reorder the terms: 10 + x + -0.6x2 = -7 + 7 + -1x + x + 0.6x2 + -0.6x2 Combine like terms: -7 + 7 = 0 10 + x + -0.6x2 = 0 + -1x + x + 0.6x2 + -0.6x2 10 + x + -0.6x2 = -1x + x + 0.6x2 + -0.6x2 Combine like terms: -1x + x = 0 10 + x + -0.6x2 = 0 + 0.6x2 + -0.6x2 10 + x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 10 + x + -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'. -16.66666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -1.666666667x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -1.666666667x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 16.66666667 -1.666666667x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -1.666666667x + x2 = 16.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1.666666667x + 0.25 + x2 = 16.66666667 + 0.25 Reorder the terms: 0.25 + -1.666666667x + x2 = 16.66666667 + 0.25 Combine like terms: 16.66666667 + 0.25 = 16.91666667 0.25 + -1.666666667x + x2 = 16.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 16.91666667 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (x + 0.5) equal to 4.11298756 and -4.11298756.Subproblem 1
x + 0.5 = 4.11298756 Simplifying x + 0.5 = 4.11298756 Reorder the terms: 0.5 + x = 4.11298756 Solving 0.5 + x = 4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.11298756 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.11298756 + -0.5 x = 4.11298756 + -0.5 Combine like terms: 4.11298756 + -0.5 = 3.61298756 x = 3.61298756 Simplifying x = 3.61298756Subproblem 2
x + 0.5 = -4.11298756 Simplifying x + 0.5 = -4.11298756 Reorder the terms: 0.5 + x = -4.11298756 Solving 0.5 + x = -4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.11298756 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.11298756 + -0.5 x = -4.11298756 + -0.5 Combine like terms: -4.11298756 + -0.5 = -4.61298756 x = -4.61298756 Simplifying x = -4.61298756Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.61298756, -4.61298756}
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