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Simplifying 5x2 + 60x + -2250 = 0 Reorder the terms: -2250 + 60x + 5x2 = 0 Solving -2250 + 60x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-450 + 12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-450 + 12x + x2)' equal to zero and attempt to solve: Simplifying -450 + 12x + x2 = 0 Solving -450 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 12x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 12x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 12x + x2 = 0 + 450 12x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 12x + x2 = 450 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 450 + 36 Reorder the terms: 36 + 12x + x2 = 450 + 36 Combine like terms: 450 + 36 = 486 36 + 12x + x2 = 486 Factor a perfect square on the left side: (x + 6)(x + 6) = 486 Calculate the square root of the right side: 22.045407685 Break this problem into two subproblems by setting (x + 6) equal to 22.045407685 and -22.045407685.Subproblem 1
x + 6 = 22.045407685 Simplifying x + 6 = 22.045407685 Reorder the terms: 6 + x = 22.045407685 Solving 6 + x = 22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 22.045407685 + -6 Combine like terms: 6 + -6 = 0 0 + x = 22.045407685 + -6 x = 22.045407685 + -6 Combine like terms: 22.045407685 + -6 = 16.045407685 x = 16.045407685 Simplifying x = 16.045407685Subproblem 2
x + 6 = -22.045407685 Simplifying x + 6 = -22.045407685 Reorder the terms: 6 + x = -22.045407685 Solving 6 + x = -22.045407685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -22.045407685 + -6 Combine like terms: 6 + -6 = 0 0 + x = -22.045407685 + -6 x = -22.045407685 + -6 Combine like terms: -22.045407685 + -6 = -28.045407685 x = -28.045407685 Simplifying x = -28.045407685Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.045407685, -28.045407685}Solution
x = {16.045407685, -28.045407685}
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