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Simplifying 5x2 + -6x + -192 = 0 Reorder the terms: -192 + -6x + 5x2 = 0 Solving -192 + -6x + 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 + -1.2x + x2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + -1.2x + 38.4 + x2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + -1.2x + x2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + -1.2x + x2 = 0 + 38.4 -1.2x + x2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 -1.2x + x2 = 38.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 38.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 38.4 + 0.36 Combine like terms: 38.4 + 0.36 = 38.76 0.36 + -1.2x + x2 = 38.76 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 38.76 Calculate the square root of the right side: 6.225752967 Break this problem into two subproblems by setting (x + -0.6) equal to 6.225752967 and -6.225752967.Subproblem 1
x + -0.6 = 6.225752967 Simplifying x + -0.6 = 6.225752967 Reorder the terms: -0.6 + x = 6.225752967 Solving -0.6 + x = 6.225752967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 6.225752967 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 6.225752967 + 0.6 x = 6.225752967 + 0.6 Combine like terms: 6.225752967 + 0.6 = 6.825752967 x = 6.825752967 Simplifying x = 6.825752967Subproblem 2
x + -0.6 = -6.225752967 Simplifying x + -0.6 = -6.225752967 Reorder the terms: -0.6 + x = -6.225752967 Solving -0.6 + x = -6.225752967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -6.225752967 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -6.225752967 + 0.6 x = -6.225752967 + 0.6 Combine like terms: -6.225752967 + 0.6 = -5.625752967 x = -5.625752967 Simplifying x = -5.625752967Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.825752967, -5.625752967}
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