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Simplifying 16x2 + -72x + 75 = 0 Reorder the terms: 75 + -72x + 16x2 = 0 Solving 75 + -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'. 4.6875 + -4.5x + x2 = 0 Move the constant term to the right: Add '-4.6875' to each side of the equation. 4.6875 + -4.5x + -4.6875 + x2 = 0 + -4.6875 Reorder the terms: 4.6875 + -4.6875 + -4.5x + x2 = 0 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + -4.5x + x2 = 0 + -4.6875 -4.5x + x2 = 0 + -4.6875 Combine like terms: 0 + -4.6875 = -4.6875 -4.5x + x2 = -4.6875 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 = -4.6875 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -4.6875 + 5.0625 Combine like terms: -4.6875 + 5.0625 = 0.375 5.0625 + -4.5x + x2 = 0.375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + -2.25) equal to 0.612372436 and -0.612372436.Subproblem 1
x + -2.25 = 0.612372436 Simplifying x + -2.25 = 0.612372436 Reorder the terms: -2.25 + x = 0.612372436 Solving -2.25 + x = 0.612372436 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 = 0.612372436 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 0.612372436 + 2.25 x = 0.612372436 + 2.25 Combine like terms: 0.612372436 + 2.25 = 2.862372436 x = 2.862372436 Simplifying x = 2.862372436Subproblem 2
x + -2.25 = -0.612372436 Simplifying x + -2.25 = -0.612372436 Reorder the terms: -2.25 + x = -0.612372436 Solving -2.25 + x = -0.612372436 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 = -0.612372436 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -0.612372436 + 2.25 x = -0.612372436 + 2.25 Combine like terms: -0.612372436 + 2.25 = 1.637627564 x = 1.637627564 Simplifying x = 1.637627564Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.862372436, 1.637627564}
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