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Simplifying 2x2 + 30x = 52 Reorder the terms: 30x + 2x2 = 52 Solving 30x + 2x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 30x + 2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + 15x + x2)' equal to zero and attempt to solve: Simplifying -26 + 15x + x2 = 0 Solving -26 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 15x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 15x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 15x + x2 = 0 + 26 15x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 15x + x2 = 26 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 = 26 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 26 + 56.25 Combine like terms: 26 + 56.25 = 82.25 56.25 + 15x + x2 = 82.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + 7.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + 7.5 = 9.069178574 Simplifying x + 7.5 = 9.069178574 Reorder the terms: 7.5 + x = 9.069178574 Solving 7.5 + x = 9.069178574 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 = 9.069178574 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.069178574 + -7.5 x = 9.069178574 + -7.5 Combine like terms: 9.069178574 + -7.5 = 1.569178574 x = 1.569178574 Simplifying x = 1.569178574Subproblem 2
x + 7.5 = -9.069178574 Simplifying x + 7.5 = -9.069178574 Reorder the terms: 7.5 + x = -9.069178574 Solving 7.5 + x = -9.069178574 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 = -9.069178574 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.069178574 + -7.5 x = -9.069178574 + -7.5 Combine like terms: -9.069178574 + -7.5 = -16.569178574 x = -16.569178574 Simplifying x = -16.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.569178574, -16.569178574}Solution
x = {1.569178574, -16.569178574}
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