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Simplifying -16x2 + 72x + 5 = 10 Reorder the terms: 5 + 72x + -16x2 = 10 Solving 5 + 72x + -16x2 = 10 Solving for variable 'x'. Reorder the terms: 5 + -10 + 72x + -16x2 = 10 + -10 Combine like terms: 5 + -10 = -5 -5 + 72x + -16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -5 + 72x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.3125 + -4.5x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -4.5x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -4.5x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -4.5x + x2 = 0 + -0.3125 -4.5x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -4.5x + x2 = -0.3125 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 = -0.3125 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -0.3125 + 5.0625 Combine like terms: -0.3125 + 5.0625 = 4.75 5.0625 + -4.5x + x2 = 4.75 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -2.25) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -2.25 = 2.179449472 Simplifying x + -2.25 = 2.179449472 Reorder the terms: -2.25 + x = 2.179449472 Solving -2.25 + x = 2.179449472 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 = 2.179449472 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.179449472 + 2.25 x = 2.179449472 + 2.25 Combine like terms: 2.179449472 + 2.25 = 4.429449472 x = 4.429449472 Simplifying x = 4.429449472Subproblem 2
x + -2.25 = -2.179449472 Simplifying x + -2.25 = -2.179449472 Reorder the terms: -2.25 + x = -2.179449472 Solving -2.25 + x = -2.179449472 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 = -2.179449472 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.179449472 + 2.25 x = -2.179449472 + 2.25 Combine like terms: -2.179449472 + 2.25 = 0.070550528 x = 0.070550528 Simplifying x = 0.070550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.429449472, 0.070550528}
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