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Simplifying 4x2 + 70x = 300 Reorder the terms: 70x + 4x2 = 300 Solving 70x + 4x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 70x + 4x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 70x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-150 + 35x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-150 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -150 + 35x + 2x2 = 0 Solving -150 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -75 + 17.5x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 17.5x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 17.5x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 17.5x + x2 = 0 + 75 17.5x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 17.5x + x2 = 75 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = 75 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 75 + 76.5625 Combine like terms: 75 + 76.5625 = 151.5625 76.5625 + 17.5x + x2 = 151.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 151.5625 Calculate the square root of the right side: 12.311072252 Break this problem into two subproblems by setting (x + 8.75) equal to 12.311072252 and -12.311072252.Subproblem 1
x + 8.75 = 12.311072252 Simplifying x + 8.75 = 12.311072252 Reorder the terms: 8.75 + x = 12.311072252 Solving 8.75 + x = 12.311072252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 12.311072252 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 12.311072252 + -8.75 x = 12.311072252 + -8.75 Combine like terms: 12.311072252 + -8.75 = 3.561072252 x = 3.561072252 Simplifying x = 3.561072252Subproblem 2
x + 8.75 = -12.311072252 Simplifying x + 8.75 = -12.311072252 Reorder the terms: 8.75 + x = -12.311072252 Solving 8.75 + x = -12.311072252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -12.311072252 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -12.311072252 + -8.75 x = -12.311072252 + -8.75 Combine like terms: -12.311072252 + -8.75 = -21.061072252 x = -21.061072252 Simplifying x = -21.061072252Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.561072252, -21.061072252}Solution
x = {3.561072252, -21.061072252}
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