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Simplifying 98 = 5x + 4.905x2 Solving 98 = 5x + 4.905x2 Solving for variable 'x'. Reorder the terms: 98 + -5x + -4.905x2 = 5x + -5x + 4.905x2 + -4.905x2 Combine like terms: 5x + -5x = 0 98 + -5x + -4.905x2 = 0 + 4.905x2 + -4.905x2 98 + -5x + -4.905x2 = 4.905x2 + -4.905x2 Combine like terms: 4.905x2 + -4.905x2 = 0.000 98 + -5x + -4.905x2 = 0.000 Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -19.97961264 + 1.019367992x + x2 = 0 Move the constant term to the right: Add '19.97961264' to each side of the equation. -19.97961264 + 1.019367992x + 19.97961264 + x2 = 0 + 19.97961264 Reorder the terms: -19.97961264 + 19.97961264 + 1.019367992x + x2 = 0 + 19.97961264 Combine like terms: -19.97961264 + 19.97961264 = 0.00000000 0.00000000 + 1.019367992x + x2 = 0 + 19.97961264 1.019367992x + x2 = 0 + 19.97961264 Combine like terms: 0 + 19.97961264 = 19.97961264 1.019367992x + x2 = 19.97961264 The x term is 1.019367992x. Take half its coefficient (0.509683996). Square it (0.2597777758) and add it to both sides. Add '0.2597777758' to each side of the equation. 1.019367992x + 0.2597777758 + x2 = 19.97961264 + 0.2597777758 Reorder the terms: 0.2597777758 + 1.019367992x + x2 = 19.97961264 + 0.2597777758 Combine like terms: 19.97961264 + 0.2597777758 = 20.2393904158 0.2597777758 + 1.019367992x + x2 = 20.2393904158 Factor a perfect square on the left side: (x + 0.509683996)(x + 0.509683996) = 20.2393904158 Calculate the square root of the right side: 4.498821003 Break this problem into two subproblems by setting (x + 0.509683996) equal to 4.498821003 and -4.498821003.Subproblem 1
x + 0.509683996 = 4.498821003 Simplifying x + 0.509683996 = 4.498821003 Reorder the terms: 0.509683996 + x = 4.498821003 Solving 0.509683996 + x = 4.498821003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.509683996' to each side of the equation. 0.509683996 + -0.509683996 + x = 4.498821003 + -0.509683996 Combine like terms: 0.509683996 + -0.509683996 = 0.000000000 0.000000000 + x = 4.498821003 + -0.509683996 x = 4.498821003 + -0.509683996 Combine like terms: 4.498821003 + -0.509683996 = 3.989137007 x = 3.989137007 Simplifying x = 3.989137007Subproblem 2
x + 0.509683996 = -4.498821003 Simplifying x + 0.509683996 = -4.498821003 Reorder the terms: 0.509683996 + x = -4.498821003 Solving 0.509683996 + x = -4.498821003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.509683996' to each side of the equation. 0.509683996 + -0.509683996 + x = -4.498821003 + -0.509683996 Combine like terms: 0.509683996 + -0.509683996 = 0.000000000 0.000000000 + x = -4.498821003 + -0.509683996 x = -4.498821003 + -0.509683996 Combine like terms: -4.498821003 + -0.509683996 = -5.008504999 x = -5.008504999 Simplifying x = -5.008504999Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.989137007, -5.008504999}
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