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Simplifying 5x2 + 8x + -192 = 0 Reorder the terms: -192 + 8x + 5x2 = 0 Solving -192 + 8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -38.4 + 1.6x + x2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + 1.6x + 38.4 + x2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + 1.6x + x2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + 1.6x + x2 = 0 + 38.4 1.6x + x2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 1.6x + x2 = 38.4 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 = 38.4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 38.4 + 0.64 Combine like terms: 38.4 + 0.64 = 39.04 0.64 + 1.6x + x2 = 39.04 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 39.04 Calculate the square root of the right side: 6.248199741 Break this problem into two subproblems by setting (x + 0.8) equal to 6.248199741 and -6.248199741.Subproblem 1
x + 0.8 = 6.248199741 Simplifying x + 0.8 = 6.248199741 Reorder the terms: 0.8 + x = 6.248199741 Solving 0.8 + x = 6.248199741 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 = 6.248199741 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 6.248199741 + -0.8 x = 6.248199741 + -0.8 Combine like terms: 6.248199741 + -0.8 = 5.448199741 x = 5.448199741 Simplifying x = 5.448199741Subproblem 2
x + 0.8 = -6.248199741 Simplifying x + 0.8 = -6.248199741 Reorder the terms: 0.8 + x = -6.248199741 Solving 0.8 + x = -6.248199741 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 = -6.248199741 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -6.248199741 + -0.8 x = -6.248199741 + -0.8 Combine like terms: -6.248199741 + -0.8 = -7.048199741 x = -7.048199741 Simplifying x = -7.048199741Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.448199741, -7.048199741}
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