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Simplifying 5x2 + 3x + -120 = 0 Reorder the terms: -120 + 3x + 5x2 = 0 Solving -120 + 3x + 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 + 0.6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 0.6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 0.6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 0.6x + x2 = 0 + 24 0.6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 0.6x + x2 = 24 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 24 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 24 + 0.09 Combine like terms: 24 + 0.09 = 24.09 0.09 + 0.6x + x2 = 24.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 24.09 Calculate the square root of the right side: 4.908156477 Break this problem into two subproblems by setting (x + 0.3) equal to 4.908156477 and -4.908156477.Subproblem 1
x + 0.3 = 4.908156477 Simplifying x + 0.3 = 4.908156477 Reorder the terms: 0.3 + x = 4.908156477 Solving 0.3 + x = 4.908156477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 4.908156477 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 4.908156477 + -0.3 x = 4.908156477 + -0.3 Combine like terms: 4.908156477 + -0.3 = 4.608156477 x = 4.608156477 Simplifying x = 4.608156477Subproblem 2
x + 0.3 = -4.908156477 Simplifying x + 0.3 = -4.908156477 Reorder the terms: 0.3 + x = -4.908156477 Solving 0.3 + x = -4.908156477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -4.908156477 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -4.908156477 + -0.3 x = -4.908156477 + -0.3 Combine like terms: -4.908156477 + -0.3 = -5.208156477 x = -5.208156477 Simplifying x = -5.208156477Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.608156477, -5.208156477}
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