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Simplifying 4x2 + 70x = 414 Reorder the terms: 70x + 4x2 = 414 Solving 70x + 4x2 = 414 Solving for variable 'x'. Reorder the terms: -414 + 70x + 4x2 = 414 + -414 Combine like terms: 414 + -414 = 0 -414 + 70x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-207 + 35x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-207 + 35x + 2x2)' equal to zero and attempt to solve: Simplifying -207 + 35x + 2x2 = 0 Solving -207 + 35x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -103.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '103.5' to each side of the equation. -103.5 + 17.5x + 103.5 + x2 = 0 + 103.5 Reorder the terms: -103.5 + 103.5 + 17.5x + x2 = 0 + 103.5 Combine like terms: -103.5 + 103.5 = 0.0 0.0 + 17.5x + x2 = 0 + 103.5 17.5x + x2 = 0 + 103.5 Combine like terms: 0 + 103.5 = 103.5 17.5x + x2 = 103.5 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 = 103.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = 103.5 + 76.5625 Combine like terms: 103.5 + 76.5625 = 180.0625 76.5625 + 17.5x + x2 = 180.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 180.0625 Calculate the square root of the right side: 13.4187369 Break this problem into two subproblems by setting (x + 8.75) equal to 13.4187369 and -13.4187369.Subproblem 1
x + 8.75 = 13.4187369 Simplifying x + 8.75 = 13.4187369 Reorder the terms: 8.75 + x = 13.4187369 Solving 8.75 + x = 13.4187369 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 = 13.4187369 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 13.4187369 + -8.75 x = 13.4187369 + -8.75 Combine like terms: 13.4187369 + -8.75 = 4.6687369 x = 4.6687369 Simplifying x = 4.6687369Subproblem 2
x + 8.75 = -13.4187369 Simplifying x + 8.75 = -13.4187369 Reorder the terms: 8.75 + x = -13.4187369 Solving 8.75 + x = -13.4187369 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 = -13.4187369 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -13.4187369 + -8.75 x = -13.4187369 + -8.75 Combine like terms: -13.4187369 + -8.75 = -22.1687369 x = -22.1687369 Simplifying x = -22.1687369Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6687369, -22.1687369}Solution
x = {4.6687369, -22.1687369}
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