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Simplifying 0 = -1.225x2 + 1.73x + 1 Reorder the terms: 0 = 1 + 1.73x + -1.225x2 Solving 0 = 1 + 1.73x + -1.225x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -1.73x + 1.225x2 = 1 + 1.73x + -1.225x2 + -1 + -1.73x + 1.225x2 Reorder the terms: -1 + -1.73x + 1.225x2 = 1 + -1 + 1.73x + -1.73x + -1.225x2 + 1.225x2 Combine like terms: 1 + -1 = 0 -1 + -1.73x + 1.225x2 = 0 + 1.73x + -1.73x + -1.225x2 + 1.225x2 -1 + -1.73x + 1.225x2 = 1.73x + -1.73x + -1.225x2 + 1.225x2 Combine like terms: 1.73x + -1.73x = 0.00 -1 + -1.73x + 1.225x2 = 0.00 + -1.225x2 + 1.225x2 -1 + -1.73x + 1.225x2 = -1.225x2 + 1.225x2 Combine like terms: -1.225x2 + 1.225x2 = 0.000 -1 + -1.73x + 1.225x2 = 0.000 Begin completing the square. Divide all terms by 1.225 the coefficient of the squared term: Divide each side by '1.225'. -0.8163265306 + -1.412244898x + x2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -1.412244898x + 0.8163265306 + x2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -1.412244898x + x2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -1.412244898x + x2 = 0 + 0.8163265306 -1.412244898x + x2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -1.412244898x + x2 = 0.8163265306 The x term is -1.412244898x. Take half its coefficient (-0.706122449). Square it (0.4986089130) and add it to both sides. Add '0.4986089130' to each side of the equation. -1.412244898x + 0.4986089130 + x2 = 0.8163265306 + 0.4986089130 Reorder the terms: 0.4986089130 + -1.412244898x + x2 = 0.8163265306 + 0.4986089130 Combine like terms: 0.8163265306 + 0.4986089130 = 1.3149354436 0.4986089130 + -1.412244898x + x2 = 1.3149354436 Factor a perfect square on the left side: (x + -0.706122449)(x + -0.706122449) = 1.3149354436 Calculate the square root of the right side: 1.146706346 Break this problem into two subproblems by setting (x + -0.706122449) equal to 1.146706346 and -1.146706346.Subproblem 1
x + -0.706122449 = 1.146706346 Simplifying x + -0.706122449 = 1.146706346 Reorder the terms: -0.706122449 + x = 1.146706346 Solving -0.706122449 + x = 1.146706346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.706122449' to each side of the equation. -0.706122449 + 0.706122449 + x = 1.146706346 + 0.706122449 Combine like terms: -0.706122449 + 0.706122449 = 0.000000000 0.000000000 + x = 1.146706346 + 0.706122449 x = 1.146706346 + 0.706122449 Combine like terms: 1.146706346 + 0.706122449 = 1.852828795 x = 1.852828795 Simplifying x = 1.852828795Subproblem 2
x + -0.706122449 = -1.146706346 Simplifying x + -0.706122449 = -1.146706346 Reorder the terms: -0.706122449 + x = -1.146706346 Solving -0.706122449 + x = -1.146706346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.706122449' to each side of the equation. -0.706122449 + 0.706122449 + x = -1.146706346 + 0.706122449 Combine like terms: -0.706122449 + 0.706122449 = 0.000000000 0.000000000 + x = -1.146706346 + 0.706122449 x = -1.146706346 + 0.706122449 Combine like terms: -1.146706346 + 0.706122449 = -0.440583897 x = -0.440583897 Simplifying x = -0.440583897Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.852828795, -0.440583897}
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