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Simplifying 3.2(x2) + -4.5x + -2 = 0 Reorder the terms: -2 + -4.5x + 3.2x2 = 0 Solving -2 + -4.5x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -0.625 + -1.40625x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1.40625x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1.40625x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1.40625x + x2 = 0 + 0.625 -1.40625x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1.40625x + x2 = 0.625 The x term is -1.40625x. Take half its coefficient (-0.703125). Square it (0.4943847656) and add it to both sides. Add '0.4943847656' to each side of the equation. -1.40625x + 0.4943847656 + x2 = 0.625 + 0.4943847656 Reorder the terms: 0.4943847656 + -1.40625x + x2 = 0.625 + 0.4943847656 Combine like terms: 0.625 + 0.4943847656 = 1.1193847656 0.4943847656 + -1.40625x + x2 = 1.1193847656 Factor a perfect square on the left side: (x + -0.703125)(x + -0.703125) = 1.1193847656 Calculate the square root of the right side: 1.058009814 Break this problem into two subproblems by setting (x + -0.703125) equal to 1.058009814 and -1.058009814.Subproblem 1
x + -0.703125 = 1.058009814 Simplifying x + -0.703125 = 1.058009814 Reorder the terms: -0.703125 + x = 1.058009814 Solving -0.703125 + x = 1.058009814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.703125' to each side of the equation. -0.703125 + 0.703125 + x = 1.058009814 + 0.703125 Combine like terms: -0.703125 + 0.703125 = 0.000000 0.000000 + x = 1.058009814 + 0.703125 x = 1.058009814 + 0.703125 Combine like terms: 1.058009814 + 0.703125 = 1.761134814 x = 1.761134814 Simplifying x = 1.761134814Subproblem 2
x + -0.703125 = -1.058009814 Simplifying x + -0.703125 = -1.058009814 Reorder the terms: -0.703125 + x = -1.058009814 Solving -0.703125 + x = -1.058009814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.703125' to each side of the equation. -0.703125 + 0.703125 + x = -1.058009814 + 0.703125 Combine like terms: -0.703125 + 0.703125 = 0.000000 0.000000 + x = -1.058009814 + 0.703125 x = -1.058009814 + 0.703125 Combine like terms: -1.058009814 + 0.703125 = -0.354884814 x = -0.354884814 Simplifying x = -0.354884814Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.761134814, -0.354884814}
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