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Simplifying 5x2 + -2x + -6 = -3 + 6x Reorder the terms: -6 + -2x + 5x2 = -3 + 6x Solving -6 + -2x + 5x2 = -3 + 6x Solving for variable 'x'. Reorder the terms: -6 + 3 + -2x + -6x + 5x2 = -3 + 6x + 3 + -6x Combine like terms: -6 + 3 = -3 -3 + -2x + -6x + 5x2 = -3 + 6x + 3 + -6x Combine like terms: -2x + -6x = -8x -3 + -8x + 5x2 = -3 + 6x + 3 + -6x Reorder the terms: -3 + -8x + 5x2 = -3 + 3 + 6x + -6x Combine like terms: -3 + 3 = 0 -3 + -8x + 5x2 = 0 + 6x + -6x -3 + -8x + 5x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.6x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.6x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.6x + x2 = 0 + 0.6 -1.6x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.6x + x2 = 0.6 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 0.6 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.6 + 0.64 Combine like terms: 0.6 + 0.64 = 1.24 0.64 + -1.6x + x2 = 1.24 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -0.8) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -0.8 = 1.113552873 Simplifying x + -0.8 = 1.113552873 Reorder the terms: -0.8 + x = 1.113552873 Solving -0.8 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.113552873 + 0.8 x = 1.113552873 + 0.8 Combine like terms: 1.113552873 + 0.8 = 1.913552873 x = 1.913552873 Simplifying x = 1.913552873Subproblem 2
x + -0.8 = -1.113552873 Simplifying x + -0.8 = -1.113552873 Reorder the terms: -0.8 + x = -1.113552873 Solving -0.8 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.113552873 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.113552873 + 0.8 x = -1.113552873 + 0.8 Combine like terms: -1.113552873 + 0.8 = -0.313552873 x = -0.313552873 Simplifying x = -0.313552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.913552873, -0.313552873}
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