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Simplifying 5x2 + 53x + -192 = 0 Reorder the terms: -192 + 53x + 5x2 = 0 Solving -192 + 53x + 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 + 10.6x + x2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + 10.6x + 38.4 + x2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + 10.6x + x2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + 10.6x + x2 = 0 + 38.4 10.6x + x2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 10.6x + x2 = 38.4 The x term is 10.6x. Take half its coefficient (5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. 10.6x + 28.09 + x2 = 38.4 + 28.09 Reorder the terms: 28.09 + 10.6x + x2 = 38.4 + 28.09 Combine like terms: 38.4 + 28.09 = 66.49 28.09 + 10.6x + x2 = 66.49 Factor a perfect square on the left side: (x + 5.3)(x + 5.3) = 66.49 Calculate the square root of the right side: 8.154140053 Break this problem into two subproblems by setting (x + 5.3) equal to 8.154140053 and -8.154140053.Subproblem 1
x + 5.3 = 8.154140053 Simplifying x + 5.3 = 8.154140053 Reorder the terms: 5.3 + x = 8.154140053 Solving 5.3 + x = 8.154140053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = 8.154140053 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = 8.154140053 + -5.3 x = 8.154140053 + -5.3 Combine like terms: 8.154140053 + -5.3 = 2.854140053 x = 2.854140053 Simplifying x = 2.854140053Subproblem 2
x + 5.3 = -8.154140053 Simplifying x + 5.3 = -8.154140053 Reorder the terms: 5.3 + x = -8.154140053 Solving 5.3 + x = -8.154140053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = -8.154140053 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = -8.154140053 + -5.3 x = -8.154140053 + -5.3 Combine like terms: -8.154140053 + -5.3 = -13.454140053 x = -13.454140053 Simplifying x = -13.454140053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.854140053, -13.454140053}
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