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Simplifying 1500 + -300x + 5x2 = 0 Solving 1500 + -300x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(300 + -60x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(300 + -60x + x2)' equal to zero and attempt to solve: Simplifying 300 + -60x + x2 = 0 Solving 300 + -60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -60x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -60x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -60x + x2 = 0 + -300 -60x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -60x + x2 = -300 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -300 + 900 Reorder the terms: 900 + -60x + x2 = -300 + 900 Combine like terms: -300 + 900 = 600 900 + -60x + x2 = 600 Factor a perfect square on the left side: (x + -30)(x + -30) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + -30) equal to 24.494897428 and -24.494897428.Subproblem 1
x + -30 = 24.494897428 Simplifying x + -30 = 24.494897428 Reorder the terms: -30 + x = 24.494897428 Solving -30 + x = 24.494897428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 24.494897428 + 30 Combine like terms: -30 + 30 = 0 0 + x = 24.494897428 + 30 x = 24.494897428 + 30 Combine like terms: 24.494897428 + 30 = 54.494897428 x = 54.494897428 Simplifying x = 54.494897428Subproblem 2
x + -30 = -24.494897428 Simplifying x + -30 = -24.494897428 Reorder the terms: -30 + x = -24.494897428 Solving -30 + x = -24.494897428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -24.494897428 + 30 Combine like terms: -30 + 30 = 0 0 + x = -24.494897428 + 30 x = -24.494897428 + 30 Combine like terms: -24.494897428 + 30 = 5.505102572 x = 5.505102572 Simplifying x = 5.505102572Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.494897428, 5.505102572}Solution
x = {54.494897428, 5.505102572}
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