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Simplifying 0 = 5x2 + 57x + -32 Reorder the terms: 0 = -32 + 57x + 5x2 Solving 0 = -32 + 57x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 32 = 32 32 + -57x + -5x2 = -32 + 57x + 5x2 + 32 + -57x + -5x2 Reorder the terms: 32 + -57x + -5x2 = -32 + 32 + 57x + -57x + 5x2 + -5x2 Combine like terms: -32 + 32 = 0 32 + -57x + -5x2 = 0 + 57x + -57x + 5x2 + -5x2 32 + -57x + -5x2 = 57x + -57x + 5x2 + -5x2 Combine like terms: 57x + -57x = 0 32 + -57x + -5x2 = 0 + 5x2 + -5x2 32 + -57x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 32 + -57x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6.4 + 11.4x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 11.4x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 11.4x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 11.4x + x2 = 0 + 6.4 11.4x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 11.4x + x2 = 6.4 The x term is 11.4x. Take half its coefficient (5.7). Square it (32.49) and add it to both sides. Add '32.49' to each side of the equation. 11.4x + 32.49 + x2 = 6.4 + 32.49 Reorder the terms: 32.49 + 11.4x + x2 = 6.4 + 32.49 Combine like terms: 6.4 + 32.49 = 38.89 32.49 + 11.4x + x2 = 38.89 Factor a perfect square on the left side: (x + 5.7)(x + 5.7) = 38.89 Calculate the square root of the right side: 6.236184731 Break this problem into two subproblems by setting (x + 5.7) equal to 6.236184731 and -6.236184731.Subproblem 1
x + 5.7 = 6.236184731 Simplifying x + 5.7 = 6.236184731 Reorder the terms: 5.7 + x = 6.236184731 Solving 5.7 + x = 6.236184731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.7' to each side of the equation. 5.7 + -5.7 + x = 6.236184731 + -5.7 Combine like terms: 5.7 + -5.7 = 0.0 0.0 + x = 6.236184731 + -5.7 x = 6.236184731 + -5.7 Combine like terms: 6.236184731 + -5.7 = 0.536184731 x = 0.536184731 Simplifying x = 0.536184731Subproblem 2
x + 5.7 = -6.236184731 Simplifying x + 5.7 = -6.236184731 Reorder the terms: 5.7 + x = -6.236184731 Solving 5.7 + x = -6.236184731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.7' to each side of the equation. 5.7 + -5.7 + x = -6.236184731 + -5.7 Combine like terms: 5.7 + -5.7 = 0.0 0.0 + x = -6.236184731 + -5.7 x = -6.236184731 + -5.7 Combine like terms: -6.236184731 + -5.7 = -11.936184731 x = -11.936184731 Simplifying x = -11.936184731Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.536184731, -11.936184731}
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