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Simplifying 0 = 5x2 + 6x + -1224 Reorder the terms: 0 = -1224 + 6x + 5x2 Solving 0 = -1224 + 6x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 1224 = 1224 1224 + -6x + -5x2 = -1224 + 6x + 5x2 + 1224 + -6x + -5x2 Reorder the terms: 1224 + -6x + -5x2 = -1224 + 1224 + 6x + -6x + 5x2 + -5x2 Combine like terms: -1224 + 1224 = 0 1224 + -6x + -5x2 = 0 + 6x + -6x + 5x2 + -5x2 1224 + -6x + -5x2 = 6x + -6x + 5x2 + -5x2 Combine like terms: 6x + -6x = 0 1224 + -6x + -5x2 = 0 + 5x2 + -5x2 1224 + -6x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1224 + -6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -244.8 + 1.2x + x2 = 0 Move the constant term to the right: Add '244.8' to each side of the equation. -244.8 + 1.2x + 244.8 + x2 = 0 + 244.8 Reorder the terms: -244.8 + 244.8 + 1.2x + x2 = 0 + 244.8 Combine like terms: -244.8 + 244.8 = 0.0 0.0 + 1.2x + x2 = 0 + 244.8 1.2x + x2 = 0 + 244.8 Combine like terms: 0 + 244.8 = 244.8 1.2x + x2 = 244.8 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 = 244.8 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 244.8 + 0.36 Combine like terms: 244.8 + 0.36 = 245.16 0.36 + 1.2x + x2 = 245.16 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 245.16 Calculate the square root of the right side: 15.657586021 Break this problem into two subproblems by setting (x + 0.6) equal to 15.657586021 and -15.657586021.Subproblem 1
x + 0.6 = 15.657586021 Simplifying x + 0.6 = 15.657586021 Reorder the terms: 0.6 + x = 15.657586021 Solving 0.6 + x = 15.657586021 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 = 15.657586021 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 15.657586021 + -0.6 x = 15.657586021 + -0.6 Combine like terms: 15.657586021 + -0.6 = 15.057586021 x = 15.057586021 Simplifying x = 15.057586021Subproblem 2
x + 0.6 = -15.657586021 Simplifying x + 0.6 = -15.657586021 Reorder the terms: 0.6 + x = -15.657586021 Solving 0.6 + x = -15.657586021 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 = -15.657586021 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -15.657586021 + -0.6 x = -15.657586021 + -0.6 Combine like terms: -15.657586021 + -0.6 = -16.257586021 x = -16.257586021 Simplifying x = -16.257586021Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.057586021, -16.257586021}
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