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Simplifying 0 = -4.9x2 + 5x + 3 Reorder the terms: 0 = 3 + 5x + -4.9x2 Solving 0 = 3 + 5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -5x + 4.9x2 = 3 + 5x + -4.9x2 + -3 + -5x + 4.9x2 Reorder the terms: -3 + -5x + 4.9x2 = 3 + -3 + 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 3 + -3 = 0 -3 + -5x + 4.9x2 = 0 + 5x + -5x + -4.9x2 + 4.9x2 -3 + -5x + 4.9x2 = 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 5x + -5x = 0 -3 + -5x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -3 + -5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -3 + -5x + 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'. -0.612244898 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -1.020408163x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -1.020408163x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -1.020408163x + x2 = 0 + 0.612244898 -1.020408163x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -1.020408163x + x2 = 0.612244898 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 0.612244898 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 0.612244898 + 0.2603082048 Combine like terms: 0.612244898 + 0.2603082048 = 0.8725531028 0.2603082048 + -1.020408163x + x2 = 0.8725531028 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 0.8725531028 Calculate the square root of the right side: 0.934105509 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 0.934105509 and -0.934105509.Subproblem 1
x + -0.5102040815 = 0.934105509 Simplifying x + -0.5102040815 = 0.934105509 Reorder the terms: -0.5102040815 + x = 0.934105509 Solving -0.5102040815 + x = 0.934105509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 0.934105509 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 0.934105509 + 0.5102040815 x = 0.934105509 + 0.5102040815 Combine like terms: 0.934105509 + 0.5102040815 = 1.4443095905 x = 1.4443095905 Simplifying x = 1.4443095905Subproblem 2
x + -0.5102040815 = -0.934105509 Simplifying x + -0.5102040815 = -0.934105509 Reorder the terms: -0.5102040815 + x = -0.934105509 Solving -0.5102040815 + x = -0.934105509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -0.934105509 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -0.934105509 + 0.5102040815 x = -0.934105509 + 0.5102040815 Combine like terms: -0.934105509 + 0.5102040815 = -0.4239014275 x = -0.4239014275 Simplifying x = -0.4239014275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4443095905, -0.4239014275}
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