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Simplifying 2x2 + 30x = 750 Reorder the terms: 30x + 2x2 = 750 Solving 30x + 2x2 = 750 Solving for variable 'x'. Reorder the terms: -750 + 30x + 2x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -750 + 30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-375 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-375 + 15x + x2)' equal to zero and attempt to solve: Simplifying -375 + 15x + x2 = 0 Solving -375 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + 15x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 15x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 15x + x2 = 0 + 375 15x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 15x + x2 = 375 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 = 375 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 375 + 56.25 Combine like terms: 375 + 56.25 = 431.25 56.25 + 15x + x2 = 431.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 431.25 Calculate the square root of the right side: 20.766559657 Break this problem into two subproblems by setting (x + 7.5) equal to 20.766559657 and -20.766559657.Subproblem 1
x + 7.5 = 20.766559657 Simplifying x + 7.5 = 20.766559657 Reorder the terms: 7.5 + x = 20.766559657 Solving 7.5 + x = 20.766559657 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 = 20.766559657 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 20.766559657 + -7.5 x = 20.766559657 + -7.5 Combine like terms: 20.766559657 + -7.5 = 13.266559657 x = 13.266559657 Simplifying x = 13.266559657Subproblem 2
x + 7.5 = -20.766559657 Simplifying x + 7.5 = -20.766559657 Reorder the terms: 7.5 + x = -20.766559657 Solving 7.5 + x = -20.766559657 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 = -20.766559657 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -20.766559657 + -7.5 x = -20.766559657 + -7.5 Combine like terms: -20.766559657 + -7.5 = -28.266559657 x = -28.266559657 Simplifying x = -28.266559657Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.266559657, -28.266559657}Solution
x = {13.266559657, -28.266559657}
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