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Simplifying 0 = 4.9x2 + 4x + -10 Reorder the terms: 0 = -10 + 4x + 4.9x2 Solving 0 = -10 + 4x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -4x + -4.9x2 = -10 + 4x + 4.9x2 + 10 + -4x + -4.9x2 Reorder the terms: 10 + -4x + -4.9x2 = -10 + 10 + 4x + -4x + 4.9x2 + -4.9x2 Combine like terms: -10 + 10 = 0 10 + -4x + -4.9x2 = 0 + 4x + -4x + 4.9x2 + -4.9x2 10 + -4x + -4.9x2 = 4x + -4x + 4.9x2 + -4.9x2 Combine like terms: 4x + -4x = 0 10 + -4x + -4.9x2 = 0 + 4.9x2 + -4.9x2 10 + -4x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 10 + -4x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + 0.8163265306x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 0.8163265306x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 0.8163265306x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 0.8163265306x + x2 = 0 + 2.040816327 0.8163265306x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 0.8163265306x + x2 = 2.040816327 The x term is 0.8163265306x. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306x + 0.1665972511 + x2 = 2.040816327 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306x + x2 = 2.040816327 + 0.1665972511 Combine like terms: 2.040816327 + 0.1665972511 = 2.2074135781 0.1665972511 + 0.8163265306x + x2 = 2.2074135781 Factor a perfect square on the left side: (x + 0.4081632653)(x + 0.4081632653) = 2.2074135781 Calculate the square root of the right side: 1.485736712 Break this problem into two subproblems by setting (x + 0.4081632653) equal to 1.485736712 and -1.485736712.Subproblem 1
x + 0.4081632653 = 1.485736712 Simplifying x + 0.4081632653 = 1.485736712 Reorder the terms: 0.4081632653 + x = 1.485736712 Solving 0.4081632653 + x = 1.485736712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = 1.485736712 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = 1.485736712 + -0.4081632653 x = 1.485736712 + -0.4081632653 Combine like terms: 1.485736712 + -0.4081632653 = 1.0775734467 x = 1.0775734467 Simplifying x = 1.0775734467Subproblem 2
x + 0.4081632653 = -1.485736712 Simplifying x + 0.4081632653 = -1.485736712 Reorder the terms: 0.4081632653 + x = -1.485736712 Solving 0.4081632653 + x = -1.485736712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + x = -1.485736712 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + x = -1.485736712 + -0.4081632653 x = -1.485736712 + -0.4081632653 Combine like terms: -1.485736712 + -0.4081632653 = -1.8938999773 x = -1.8938999773 Simplifying x = -1.8938999773Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0775734467, -1.8938999773}
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