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Simplifying 3x2 + -45x + 15 = 0 Reorder the terms: 15 + -45x + 3x2 = 0 Solving 15 + -45x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -15x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -15x + x2)' equal to zero and attempt to solve: Simplifying 5 + -15x + x2 = 0 Solving 5 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -15x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -15x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -15x + x2 = 0 + -5 -15x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -15x + x2 = -5 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 = -5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -5 + 56.25 Combine like terms: -5 + 56.25 = 51.25 56.25 + -15x + x2 = 51.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -7.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -7.5 = 7.158910532 Simplifying x + -7.5 = 7.158910532 Reorder the terms: -7.5 + x = 7.158910532 Solving -7.5 + x = 7.158910532 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 = 7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.158910532 + 7.5 x = 7.158910532 + 7.5 Combine like terms: 7.158910532 + 7.5 = 14.658910532 x = 14.658910532 Simplifying x = 14.658910532Subproblem 2
x + -7.5 = -7.158910532 Simplifying x + -7.5 = -7.158910532 Reorder the terms: -7.5 + x = -7.158910532 Solving -7.5 + x = -7.158910532 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 = -7.158910532 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.158910532 + 7.5 x = -7.158910532 + 7.5 Combine like terms: -7.158910532 + 7.5 = 0.341089468 x = 0.341089468 Simplifying x = 0.341089468Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.658910532, 0.341089468}Solution
x = {14.658910532, 0.341089468}
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