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Simplifying 0 = 2x2 + -30x + -100 Reorder the terms: 0 = -100 + -30x + 2x2 Solving 0 = -100 + -30x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + 30x + -2x2 = -100 + -30x + 2x2 + 100 + 30x + -2x2 Reorder the terms: 100 + 30x + -2x2 = -100 + 100 + -30x + 30x + 2x2 + -2x2 Combine like terms: -100 + 100 = 0 100 + 30x + -2x2 = 0 + -30x + 30x + 2x2 + -2x2 100 + 30x + -2x2 = -30x + 30x + 2x2 + -2x2 Combine like terms: -30x + 30x = 0 100 + 30x + -2x2 = 0 + 2x2 + -2x2 100 + 30x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 100 + 30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 15x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 50 + 15x + -1x2 = 0 Solving 50 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -15x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -15x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -15x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15x + x2 = 0 + 50 -15x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15x + x2 = 50 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 = 50 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15x + x2 = 106.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -7.5 = 10.307764064 Simplifying x + -7.5 = 10.307764064 Reorder the terms: -7.5 + x = 10.307764064 Solving -7.5 + x = 10.307764064 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 = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 10.307764064 + 7.5 x = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 x = 17.807764064 Simplifying x = 17.807764064Subproblem 2
x + -7.5 = -10.307764064 Simplifying x + -7.5 = -10.307764064 Reorder the terms: -7.5 + x = -10.307764064 Solving -7.5 + x = -10.307764064 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 = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -10.307764064 + 7.5 x = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 x = -2.807764064 Simplifying x = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.807764064, -2.807764064}Solution
x = {17.807764064, -2.807764064}
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