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Simplifying -4.9x2 + 4.9x + 10 = 0 Reorder the terms: 10 + 4.9x + -4.9x2 = 0 Solving 10 + 4.9x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + -1x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1x + x2 = 0 + 2.040816327 -1x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1x + x2 = 2.040816327 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.040816327 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.040816327 + 0.25 Combine like terms: 2.040816327 + 0.25 = 2.290816327 0.25 + -1x + x2 = 2.290816327 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.290816327 Calculate the square root of the right side: 1.513544293 Break this problem into two subproblems by setting (x + -0.5) equal to 1.513544293 and -1.513544293.Subproblem 1
x + -0.5 = 1.513544293 Simplifying x + -0.5 = 1.513544293 Reorder the terms: -0.5 + x = 1.513544293 Solving -0.5 + x = 1.513544293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.513544293 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.513544293 + 0.5 x = 1.513544293 + 0.5 Combine like terms: 1.513544293 + 0.5 = 2.013544293 x = 2.013544293 Simplifying x = 2.013544293Subproblem 2
x + -0.5 = -1.513544293 Simplifying x + -0.5 = -1.513544293 Reorder the terms: -0.5 + x = -1.513544293 Solving -0.5 + x = -1.513544293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.513544293 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.513544293 + 0.5 x = -1.513544293 + 0.5 Combine like terms: -1.513544293 + 0.5 = -1.013544293 x = -1.013544293 Simplifying x = -1.013544293Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.013544293, -1.013544293}
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