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Simplifying 5x * x + -410x + 300 = 300x Multiply x * x 5x2 + -410x + 300 = 300x Reorder the terms: 300 + -410x + 5x2 = 300x Solving 300 + -410x + 5x2 = 300x Solving for variable 'x'. Reorder the terms: 300 + -410x + -300x + 5x2 = 300x + -300x Combine like terms: -410x + -300x = -710x 300 + -710x + 5x2 = 300x + -300x Combine like terms: 300x + -300x = 0 300 + -710x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(60 + -142x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(60 + -142x + x2)' equal to zero and attempt to solve: Simplifying 60 + -142x + x2 = 0 Solving 60 + -142x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -142x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -142x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -142x + x2 = 0 + -60 -142x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -142x + x2 = -60 The x term is -142x. Take half its coefficient (-71). Square it (5041) and add it to both sides. Add '5041' to each side of the equation. -142x + 5041 + x2 = -60 + 5041 Reorder the terms: 5041 + -142x + x2 = -60 + 5041 Combine like terms: -60 + 5041 = 4981 5041 + -142x + x2 = 4981 Factor a perfect square on the left side: (x + -71)(x + -71) = 4981 Calculate the square root of the right side: 70.576199954 Break this problem into two subproblems by setting (x + -71) equal to 70.576199954 and -70.576199954.Subproblem 1
x + -71 = 70.576199954 Simplifying x + -71 = 70.576199954 Reorder the terms: -71 + x = 70.576199954 Solving -71 + x = 70.576199954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71' to each side of the equation. -71 + 71 + x = 70.576199954 + 71 Combine like terms: -71 + 71 = 0 0 + x = 70.576199954 + 71 x = 70.576199954 + 71 Combine like terms: 70.576199954 + 71 = 141.576199954 x = 141.576199954 Simplifying x = 141.576199954Subproblem 2
x + -71 = -70.576199954 Simplifying x + -71 = -70.576199954 Reorder the terms: -71 + x = -70.576199954 Solving -71 + x = -70.576199954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71' to each side of the equation. -71 + 71 + x = -70.576199954 + 71 Combine like terms: -71 + 71 = 0 0 + x = -70.576199954 + 71 x = -70.576199954 + 71 Combine like terms: -70.576199954 + 71 = 0.423800046 x = 0.423800046 Simplifying x = 0.423800046Solution
The solution to the problem is based on the solutions from the subproblems. x = {141.576199954, 0.423800046}Solution
x = {141.576199954, 0.423800046}
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