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Simplifying 4x2 + 6x + -121 = 0 Reorder the terms: -121 + 6x + 4x2 = 0 Solving -121 + 6x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -30.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '30.25' to each side of the equation. -30.25 + 1.5x + 30.25 + x2 = 0 + 30.25 Reorder the terms: -30.25 + 30.25 + 1.5x + x2 = 0 + 30.25 Combine like terms: -30.25 + 30.25 = 0.00 0.00 + 1.5x + x2 = 0 + 30.25 1.5x + x2 = 0 + 30.25 Combine like terms: 0 + 30.25 = 30.25 1.5x + x2 = 30.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 30.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 30.25 + 0.5625 Combine like terms: 30.25 + 0.5625 = 30.8125 0.5625 + 1.5x + x2 = 30.8125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 30.8125 Calculate the square root of the right side: 5.550900828 Break this problem into two subproblems by setting (x + 0.75) equal to 5.550900828 and -5.550900828.Subproblem 1
x + 0.75 = 5.550900828 Simplifying x + 0.75 = 5.550900828 Reorder the terms: 0.75 + x = 5.550900828 Solving 0.75 + x = 5.550900828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.550900828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.550900828 + -0.75 x = 5.550900828 + -0.75 Combine like terms: 5.550900828 + -0.75 = 4.800900828 x = 4.800900828 Simplifying x = 4.800900828Subproblem 2
x + 0.75 = -5.550900828 Simplifying x + 0.75 = -5.550900828 Reorder the terms: 0.75 + x = -5.550900828 Solving 0.75 + x = -5.550900828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.550900828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.550900828 + -0.75 x = -5.550900828 + -0.75 Combine like terms: -5.550900828 + -0.75 = -6.300900828 x = -6.300900828 Simplifying x = -6.300900828Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.800900828, -6.300900828}
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