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Simplifying 5x2 + 15x + -245 = 0 Reorder the terms: -245 + 15x + 5x2 = 0 Solving -245 + 15x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-49 + 3x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-49 + 3x + x2)' equal to zero and attempt to solve: Simplifying -49 + 3x + x2 = 0 Solving -49 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 3x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 3x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 3x + x2 = 0 + 49 3x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 3x + x2 = 49 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 49 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + 3x + x2 = 51.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 1.5 = 7.158910532 Simplifying x + 1.5 = 7.158910532 Reorder the terms: 1.5 + x = 7.158910532 Solving 1.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.158910532 + -1.5 x = 7.158910532 + -1.5 Combine like terms: 7.158910532 + -1.5 = 5.658910532 x = 5.658910532 Simplifying x = 5.658910532Subproblem 2
x + 1.5 = -7.158910532 Simplifying x + 1.5 = -7.158910532 Reorder the terms: 1.5 + x = -7.158910532 Solving 1.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.158910532 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.158910532 + -1.5 x = -7.158910532 + -1.5 Combine like terms: -7.158910532 + -1.5 = -8.658910532 x = -8.658910532 Simplifying x = -8.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.658910532, -8.658910532}Solution
x = {5.658910532, -8.658910532}
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