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Simplifying -1 = -5x2 + -3x + 3 Reorder the terms: -1 = 3 + -3x + -5x2 Solving -1 = 3 + -3x + -5x2 Solving for variable 'x'. Combine like terms: -1 + -3 = -4 -4 + 3x + 5x2 = 3 + -3x + -5x2 + -3 + 3x + 5x2 Reorder the terms: -4 + 3x + 5x2 = 3 + -3 + -3x + 3x + -5x2 + 5x2 Combine like terms: 3 + -3 = 0 -4 + 3x + 5x2 = 0 + -3x + 3x + -5x2 + 5x2 -4 + 3x + 5x2 = -3x + 3x + -5x2 + 5x2 Combine like terms: -3x + 3x = 0 -4 + 3x + 5x2 = 0 + -5x2 + 5x2 -4 + 3x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -4 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.6x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.6x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.6x + x2 = 0 + 0.8 0.6x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.6x + x2 = 0.8 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + 0.6x + x2 = 0.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + 0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
x + 0.3 = 0.943398113 Simplifying x + 0.3 = 0.943398113 Reorder the terms: 0.3 + x = 0.943398113 Solving 0.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.943398113 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.943398113 + -0.3 x = 0.943398113 + -0.3 Combine like terms: 0.943398113 + -0.3 = 0.643398113 x = 0.643398113 Simplifying x = 0.643398113Subproblem 2
x + 0.3 = -0.943398113 Simplifying x + 0.3 = -0.943398113 Reorder the terms: 0.3 + x = -0.943398113 Solving 0.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.943398113 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.943398113 + -0.3 x = -0.943398113 + -0.3 Combine like terms: -0.943398113 + -0.3 = -1.243398113 x = -1.243398113 Simplifying x = -1.243398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.643398113, -1.243398113}
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