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Simplifying 4x2 + 70x + -1000 = 0 Reorder the terms: -1000 + 70x + 4x2 = 0 Solving -1000 + 70x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-500 + 35x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-500 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -500 + 35x + 2x2 = 0 Solving -500 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -250 + 17.5x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 17.5x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 17.5x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 17.5x + x2 = 0 + 250 17.5x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 17.5x + x2 = 250 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 = 250 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 250 + 76.5625 Combine like terms: 250 + 76.5625 = 326.5625 76.5625 + 17.5x + x2 = 326.5625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 326.5625 Calculate the square root of the right side: 18.071040369 Break this problem into two subproblems by setting (x + 8.75) equal to 18.071040369 and -18.071040369.Subproblem 1
x + 8.75 = 18.071040369 Simplifying x + 8.75 = 18.071040369 Reorder the terms: 8.75 + x = 18.071040369 Solving 8.75 + x = 18.071040369 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 = 18.071040369 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 18.071040369 + -8.75 x = 18.071040369 + -8.75 Combine like terms: 18.071040369 + -8.75 = 9.321040369 x = 9.321040369 Simplifying x = 9.321040369Subproblem 2
x + 8.75 = -18.071040369 Simplifying x + 8.75 = -18.071040369 Reorder the terms: 8.75 + x = -18.071040369 Solving 8.75 + x = -18.071040369 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 = -18.071040369 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -18.071040369 + -8.75 x = -18.071040369 + -8.75 Combine like terms: -18.071040369 + -8.75 = -26.821040369 x = -26.821040369 Simplifying x = -26.821040369Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.321040369, -26.821040369}Solution
x = {9.321040369, -26.821040369}
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