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Simplifying -4.9x2 + 9.9x + -5 = 0 Reorder the terms: -5 + 9.9x + -4.9x2 = 0 Solving -5 + 9.9x + -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'. 1.020408163 + -2.020408163x + x2 = 0 Move the constant term to the right: Add '-1.020408163' to each side of the equation. 1.020408163 + -2.020408163x + -1.020408163 + x2 = 0 + -1.020408163 Reorder the terms: 1.020408163 + -1.020408163 + -2.020408163x + x2 = 0 + -1.020408163 Combine like terms: 1.020408163 + -1.020408163 = 0.000000000 0.000000000 + -2.020408163x + x2 = 0 + -1.020408163 -2.020408163x + x2 = 0 + -1.020408163 Combine like terms: 0 + -1.020408163 = -1.020408163 -2.020408163x + x2 = -1.020408163 The x term is -2.020408163x. Take half its coefficient (-1.010204082). Square it (1.020512287) and add it to both sides. Add '1.020512287' to each side of the equation. -2.020408163x + 1.020512287 + x2 = -1.020408163 + 1.020512287 Reorder the terms: 1.020512287 + -2.020408163x + x2 = -1.020408163 + 1.020512287 Combine like terms: -1.020408163 + 1.020512287 = 0.000104124 1.020512287 + -2.020408163x + x2 = 0.000104124 Factor a perfect square on the left side: (x + -1.010204082)(x + -1.010204082) = 0.000104124 Calculate the square root of the right side: 0.010204117 Break this problem into two subproblems by setting (x + -1.010204082) equal to 0.010204117 and -0.010204117.Subproblem 1
x + -1.010204082 = 0.010204117 Simplifying x + -1.010204082 = 0.010204117 Reorder the terms: -1.010204082 + x = 0.010204117 Solving -1.010204082 + x = 0.010204117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.010204082' to each side of the equation. -1.010204082 + 1.010204082 + x = 0.010204117 + 1.010204082 Combine like terms: -1.010204082 + 1.010204082 = 0.000000000 0.000000000 + x = 0.010204117 + 1.010204082 x = 0.010204117 + 1.010204082 Combine like terms: 0.010204117 + 1.010204082 = 1.020408199 x = 1.020408199 Simplifying x = 1.020408199Subproblem 2
x + -1.010204082 = -0.010204117 Simplifying x + -1.010204082 = -0.010204117 Reorder the terms: -1.010204082 + x = -0.010204117 Solving -1.010204082 + x = -0.010204117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.010204082' to each side of the equation. -1.010204082 + 1.010204082 + x = -0.010204117 + 1.010204082 Combine like terms: -1.010204082 + 1.010204082 = 0.000000000 0.000000000 + x = -0.010204117 + 1.010204082 x = -0.010204117 + 1.010204082 Combine like terms: -0.010204117 + 1.010204082 = 0.999999965 x = 0.999999965 Simplifying x = 0.999999965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.020408199, 0.999999965}
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