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Simplifying -4.9x2 + 2.98x + 0.12 = 0 Reorder the terms: 0.12 + 2.98x + -4.9x2 = 0 Solving 0.12 + 2.98x + -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'. -0.02448979592 + -0.6081632653x + x2 = 0 Move the constant term to the right: Add '0.02448979592' to each side of the equation. -0.02448979592 + -0.6081632653x + 0.02448979592 + x2 = 0 + 0.02448979592 Reorder the terms: -0.02448979592 + 0.02448979592 + -0.6081632653x + x2 = 0 + 0.02448979592 Combine like terms: -0.02448979592 + 0.02448979592 = 0.00000000000 0.00000000000 + -0.6081632653x + x2 = 0 + 0.02448979592 -0.6081632653x + x2 = 0 + 0.02448979592 Combine like terms: 0 + 0.02448979592 = 0.02448979592 -0.6081632653x + x2 = 0.02448979592 The x term is -0.6081632653x. Take half its coefficient (-0.3040816327). Square it (0.09246563935) and add it to both sides. Add '0.09246563935' to each side of the equation. -0.6081632653x + 0.09246563935 + x2 = 0.02448979592 + 0.09246563935 Reorder the terms: 0.09246563935 + -0.6081632653x + x2 = 0.02448979592 + 0.09246563935 Combine like terms: 0.02448979592 + 0.09246563935 = 0.11695543527 0.09246563935 + -0.6081632653x + x2 = 0.11695543527 Factor a perfect square on the left side: (x + -0.3040816327)(x + -0.3040816327) = 0.11695543527 Calculate the square root of the right side: 0.341987478 Break this problem into two subproblems by setting (x + -0.3040816327) equal to 0.341987478 and -0.341987478.Subproblem 1
x + -0.3040816327 = 0.341987478 Simplifying x + -0.3040816327 = 0.341987478 Reorder the terms: -0.3040816327 + x = 0.341987478 Solving -0.3040816327 + x = 0.341987478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3040816327' to each side of the equation. -0.3040816327 + 0.3040816327 + x = 0.341987478 + 0.3040816327 Combine like terms: -0.3040816327 + 0.3040816327 = 0.0000000000 0.0000000000 + x = 0.341987478 + 0.3040816327 x = 0.341987478 + 0.3040816327 Combine like terms: 0.341987478 + 0.3040816327 = 0.6460691107 x = 0.6460691107 Simplifying x = 0.6460691107Subproblem 2
x + -0.3040816327 = -0.341987478 Simplifying x + -0.3040816327 = -0.341987478 Reorder the terms: -0.3040816327 + x = -0.341987478 Solving -0.3040816327 + x = -0.341987478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3040816327' to each side of the equation. -0.3040816327 + 0.3040816327 + x = -0.341987478 + 0.3040816327 Combine like terms: -0.3040816327 + 0.3040816327 = 0.0000000000 0.0000000000 + x = -0.341987478 + 0.3040816327 x = -0.341987478 + 0.3040816327 Combine like terms: -0.341987478 + 0.3040816327 = -0.0379058453 x = -0.0379058453 Simplifying x = -0.0379058453Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6460691107, -0.0379058453}
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