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Simplifying 16x2 + -17x + 13 = 20x2 + -32 Reorder the terms: 13 + -17x + 16x2 = 20x2 + -32 Reorder the terms: 13 + -17x + 16x2 = -32 + 20x2 Solving 13 + -17x + 16x2 = -32 + 20x2 Solving for variable 'x'. Reorder the terms: 13 + 32 + -17x + 16x2 + -20x2 = -32 + 20x2 + 32 + -20x2 Combine like terms: 13 + 32 = 45 45 + -17x + 16x2 + -20x2 = -32 + 20x2 + 32 + -20x2 Combine like terms: 16x2 + -20x2 = -4x2 45 + -17x + -4x2 = -32 + 20x2 + 32 + -20x2 Reorder the terms: 45 + -17x + -4x2 = -32 + 32 + 20x2 + -20x2 Combine like terms: -32 + 32 = 0 45 + -17x + -4x2 = 0 + 20x2 + -20x2 45 + -17x + -4x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 45 + -17x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.25 + 4.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 4.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 4.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 4.25x + x2 = 0 + 11.25 4.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 4.25x + x2 = 11.25 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 11.25 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 11.25 + 4.515625 Combine like terms: 11.25 + 4.515625 = 15.765625 4.515625 + 4.25x + x2 = 15.765625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (x + 2.125) equal to 3.970595044 and -3.970595044.Subproblem 1
x + 2.125 = 3.970595044 Simplifying x + 2.125 = 3.970595044 Reorder the terms: 2.125 + x = 3.970595044 Solving 2.125 + x = 3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.970595044 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.970595044 + -2.125 x = 3.970595044 + -2.125 Combine like terms: 3.970595044 + -2.125 = 1.845595044 x = 1.845595044 Simplifying x = 1.845595044Subproblem 2
x + 2.125 = -3.970595044 Simplifying x + 2.125 = -3.970595044 Reorder the terms: 2.125 + x = -3.970595044 Solving 2.125 + x = -3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.970595044 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.970595044 + -2.125 x = -3.970595044 + -2.125 Combine like terms: -3.970595044 + -2.125 = -6.095595044 x = -6.095595044 Simplifying x = -6.095595044Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.845595044, -6.095595044}
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