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Simplifying -16x2 + 70x + 3 = 0 Reorder the terms: 3 + 70x + -16x2 = 0 Solving 3 + 70x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + -4.375x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -4.375x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -4.375x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -4.375x + x2 = 0 + 0.1875 -4.375x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -4.375x + x2 = 0.1875 The x term is -4.375x. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375x + 4.78515625 + x2 = 0.1875 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = 0.1875 + 4.78515625 Combine like terms: 0.1875 + 4.78515625 = 4.97265625 4.78515625 + -4.375x + x2 = 4.97265625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 4.97265625 Calculate the square root of the right side: 2.229945347 Break this problem into two subproblems by setting (x + -2.1875) equal to 2.229945347 and -2.229945347.Subproblem 1
x + -2.1875 = 2.229945347 Simplifying x + -2.1875 = 2.229945347 Reorder the terms: -2.1875 + x = 2.229945347 Solving -2.1875 + x = 2.229945347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = 2.229945347 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 2.229945347 + 2.1875 x = 2.229945347 + 2.1875 Combine like terms: 2.229945347 + 2.1875 = 4.417445347 x = 4.417445347 Simplifying x = 4.417445347Subproblem 2
x + -2.1875 = -2.229945347 Simplifying x + -2.1875 = -2.229945347 Reorder the terms: -2.1875 + x = -2.229945347 Solving -2.1875 + x = -2.229945347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = -2.229945347 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -2.229945347 + 2.1875 x = -2.229945347 + 2.1875 Combine like terms: -2.229945347 + 2.1875 = -0.042445347 x = -0.042445347 Simplifying x = -0.042445347Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.417445347, -0.042445347}
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