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Simplifying 8x2 + 30x = 704 Reorder the terms: 30x + 8x2 = 704 Solving 30x + 8x2 = 704 Solving for variable 'x'. Reorder the terms: -704 + 30x + 8x2 = 704 + -704 Combine like terms: 704 + -704 = 0 -704 + 30x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-352 + 15x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-352 + 15x + 4x2)' equal to zero and attempt to solve: Simplifying -352 + 15x + 4x2 = 0 Solving -352 + 15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -88 + 3.75x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + 3.75x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 3.75x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 3.75x + x2 = 0 + 88 3.75x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 3.75x + x2 = 88 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 88 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 88 + 3.515625 Combine like terms: 88 + 3.515625 = 91.515625 3.515625 + 3.75x + x2 = 91.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 91.515625 Calculate the square root of the right side: 9.566379932 Break this problem into two subproblems by setting (x + 1.875) equal to 9.566379932 and -9.566379932.Subproblem 1
x + 1.875 = 9.566379932 Simplifying x + 1.875 = 9.566379932 Reorder the terms: 1.875 + x = 9.566379932 Solving 1.875 + x = 9.566379932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 9.566379932 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 9.566379932 + -1.875 x = 9.566379932 + -1.875 Combine like terms: 9.566379932 + -1.875 = 7.691379932 x = 7.691379932 Simplifying x = 7.691379932Subproblem 2
x + 1.875 = -9.566379932 Simplifying x + 1.875 = -9.566379932 Reorder the terms: 1.875 + x = -9.566379932 Solving 1.875 + x = -9.566379932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -9.566379932 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -9.566379932 + -1.875 x = -9.566379932 + -1.875 Combine like terms: -9.566379932 + -1.875 = -11.441379932 x = -11.441379932 Simplifying x = -11.441379932Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.691379932, -11.441379932}Solution
x = {7.691379932, -11.441379932}
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