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Simplifying 16x2 + -72x + 63 = 0 Reorder the terms: 63 + -72x + 16x2 = 0 Solving 63 + -72x + 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'. 3.9375 + -4.5x + x2 = 0 Move the constant term to the right: Add '-3.9375' to each side of the equation. 3.9375 + -4.5x + -3.9375 + x2 = 0 + -3.9375 Reorder the terms: 3.9375 + -3.9375 + -4.5x + x2 = 0 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + -4.5x + x2 = 0 + -3.9375 -4.5x + x2 = 0 + -3.9375 Combine like terms: 0 + -3.9375 = -3.9375 -4.5x + x2 = -3.9375 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -3.9375 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -3.9375 + 5.0625 Combine like terms: -3.9375 + 5.0625 = 1.125 5.0625 + -4.5x + x2 = 1.125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (x + -2.25) equal to 1.060660172 and -1.060660172.Subproblem 1
x + -2.25 = 1.060660172 Simplifying x + -2.25 = 1.060660172 Reorder the terms: -2.25 + x = 1.060660172 Solving -2.25 + x = 1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.060660172 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.060660172 + 2.25 x = 1.060660172 + 2.25 Combine like terms: 1.060660172 + 2.25 = 3.310660172 x = 3.310660172 Simplifying x = 3.310660172Subproblem 2
x + -2.25 = -1.060660172 Simplifying x + -2.25 = -1.060660172 Reorder the terms: -2.25 + x = -1.060660172 Solving -2.25 + x = -1.060660172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.060660172 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.060660172 + 2.25 x = -1.060660172 + 2.25 Combine like terms: -1.060660172 + 2.25 = 1.189339828 x = 1.189339828 Simplifying x = 1.189339828Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.310660172, 1.189339828}
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