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Simplifying 5x2 + 6x + -120 = 0 Reorder the terms: -120 + 6x + 5x2 = 0 Solving -120 + 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'. -24 + 1.2x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.2x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 1.2x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.2x + x2 = 0 + 24 1.2x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.2x + x2 = 24 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 = 24 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 24 + 0.36 Combine like terms: 24 + 0.36 = 24.36 0.36 + 1.2x + x2 = 24.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 24.36 Calculate the square root of the right side: 4.935585072 Break this problem into two subproblems by setting (x + 0.6) equal to 4.935585072 and -4.935585072.Subproblem 1
x + 0.6 = 4.935585072 Simplifying x + 0.6 = 4.935585072 Reorder the terms: 0.6 + x = 4.935585072 Solving 0.6 + x = 4.935585072 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 = 4.935585072 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 4.935585072 + -0.6 x = 4.935585072 + -0.6 Combine like terms: 4.935585072 + -0.6 = 4.335585072 x = 4.335585072 Simplifying x = 4.335585072Subproblem 2
x + 0.6 = -4.935585072 Simplifying x + 0.6 = -4.935585072 Reorder the terms: 0.6 + x = -4.935585072 Solving 0.6 + x = -4.935585072 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 = -4.935585072 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -4.935585072 + -0.6 x = -4.935585072 + -0.6 Combine like terms: -4.935585072 + -0.6 = -5.535585072 x = -5.535585072 Simplifying x = -5.535585072Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.335585072, -5.535585072}
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