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Simplifying 32x2 + 72x + -45 = 0 Reorder the terms: -45 + 72x + 32x2 = 0 Solving -45 + 72x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.40625 + 2.25x + x2 = 0 Move the constant term to the right: Add '1.40625' to each side of the equation. -1.40625 + 2.25x + 1.40625 + x2 = 0 + 1.40625 Reorder the terms: -1.40625 + 1.40625 + 2.25x + x2 = 0 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + 2.25x + x2 = 0 + 1.40625 2.25x + x2 = 0 + 1.40625 Combine like terms: 0 + 1.40625 = 1.40625 2.25x + x2 = 1.40625 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 1.40625 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 1.40625 + 1.265625 Combine like terms: 1.40625 + 1.265625 = 2.671875 1.265625 + 2.25x + x2 = 2.671875 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 2.671875 Calculate the square root of the right side: 1.634587104 Break this problem into two subproblems by setting (x + 1.125) equal to 1.634587104 and -1.634587104.Subproblem 1
x + 1.125 = 1.634587104 Simplifying x + 1.125 = 1.634587104 Reorder the terms: 1.125 + x = 1.634587104 Solving 1.125 + x = 1.634587104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.634587104 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.634587104 + -1.125 x = 1.634587104 + -1.125 Combine like terms: 1.634587104 + -1.125 = 0.509587104 x = 0.509587104 Simplifying x = 0.509587104Subproblem 2
x + 1.125 = -1.634587104 Simplifying x + 1.125 = -1.634587104 Reorder the terms: 1.125 + x = -1.634587104 Solving 1.125 + x = -1.634587104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.634587104 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.634587104 + -1.125 x = -1.634587104 + -1.125 Combine like terms: -1.634587104 + -1.125 = -2.759587104 x = -2.759587104 Simplifying x = -2.759587104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.509587104, -2.759587104}
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