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Simplifying 150x2 + 4284x = 2324070 Reorder the terms: 4284x + 150x2 = 2324070 Solving 4284x + 150x2 = 2324070 Solving for variable 'x'. Reorder the terms: -2324070 + 4284x + 150x2 = 2324070 + -2324070 Combine like terms: 2324070 + -2324070 = 0 -2324070 + 4284x + 150x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-387345 + 714x + 25x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-387345 + 714x + 25x2)' equal to zero and attempt to solve: Simplifying -387345 + 714x + 25x2 = 0 Solving -387345 + 714x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -15493.8 + 28.56x + x2 = 0 Move the constant term to the right: Add '15493.8' to each side of the equation. -15493.8 + 28.56x + 15493.8 + x2 = 0 + 15493.8 Reorder the terms: -15493.8 + 15493.8 + 28.56x + x2 = 0 + 15493.8 Combine like terms: -15493.8 + 15493.8 = 0.0 0.0 + 28.56x + x2 = 0 + 15493.8 28.56x + x2 = 0 + 15493.8 Combine like terms: 0 + 15493.8 = 15493.8 28.56x + x2 = 15493.8 The x term is 28.56x. Take half its coefficient (14.28). Square it (203.9184) and add it to both sides. Add '203.9184' to each side of the equation. 28.56x + 203.9184 + x2 = 15493.8 + 203.9184 Reorder the terms: 203.9184 + 28.56x + x2 = 15493.8 + 203.9184 Combine like terms: 15493.8 + 203.9184 = 15697.7184 203.9184 + 28.56x + x2 = 15697.7184 Factor a perfect square on the left side: (x + 14.28)(x + 14.28) = 15697.7184 Calculate the square root of the right side: 125.290535955 Break this problem into two subproblems by setting (x + 14.28) equal to 125.290535955 and -125.290535955.Subproblem 1
x + 14.28 = 125.290535955 Simplifying x + 14.28 = 125.290535955 Reorder the terms: 14.28 + x = 125.290535955 Solving 14.28 + x = 125.290535955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.28' to each side of the equation. 14.28 + -14.28 + x = 125.290535955 + -14.28 Combine like terms: 14.28 + -14.28 = 0.00 0.00 + x = 125.290535955 + -14.28 x = 125.290535955 + -14.28 Combine like terms: 125.290535955 + -14.28 = 111.010535955 x = 111.010535955 Simplifying x = 111.010535955Subproblem 2
x + 14.28 = -125.290535955 Simplifying x + 14.28 = -125.290535955 Reorder the terms: 14.28 + x = -125.290535955 Solving 14.28 + x = -125.290535955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.28' to each side of the equation. 14.28 + -14.28 + x = -125.290535955 + -14.28 Combine like terms: 14.28 + -14.28 = 0.00 0.00 + x = -125.290535955 + -14.28 x = -125.290535955 + -14.28 Combine like terms: -125.290535955 + -14.28 = -139.570535955 x = -139.570535955 Simplifying x = -139.570535955Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.010535955, -139.570535955}Solution
x = {111.010535955, -139.570535955}
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