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Simplifying 2x2 + 30x + -60 = 0 Reorder the terms: -60 + 30x + 2x2 = 0 Solving -60 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + 15x + x2)' equal to zero and attempt to solve: Simplifying -30 + 15x + x2 = 0 Solving -30 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 15x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 15x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 15x + x2 = 0 + 30 15x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 15x + x2 = 30 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 30 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 30 + 56.25 Combine like terms: 30 + 56.25 = 86.25 56.25 + 15x + x2 = 86.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + 7.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + 7.5 = 9.287087811 Simplifying x + 7.5 = 9.287087811 Reorder the terms: 7.5 + x = 9.287087811 Solving 7.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.287087811 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.287087811 + -7.5 x = 9.287087811 + -7.5 Combine like terms: 9.287087811 + -7.5 = 1.787087811 x = 1.787087811 Simplifying x = 1.787087811Subproblem 2
x + 7.5 = -9.287087811 Simplifying x + 7.5 = -9.287087811 Reorder the terms: 7.5 + x = -9.287087811 Solving 7.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.287087811 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.287087811 + -7.5 x = -9.287087811 + -7.5 Combine like terms: -9.287087811 + -7.5 = -16.787087811 x = -16.787087811 Simplifying x = -16.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.787087811, -16.787087811}Solution
x = {1.787087811, -16.787087811}
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