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Simplifying 311.76x2 + -3054083x + 2311563221 = 0 Reorder the terms: 2311563221 + -3054083x + 311.76x2 = 0 Solving 2311563221 + -3054083x + 311.76x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 311.76 the coefficient of the squared term: Divide each side by '311.76'. 7414559.985 + -9796.263151x + x2 = 0 Move the constant term to the right: Add '-7414559.985' to each side of the equation. 7414559.985 + -9796.263151x + -7414559.985 + x2 = 0 + -7414559.985 Reorder the terms: 7414559.985 + -7414559.985 + -9796.263151x + x2 = 0 + -7414559.985 Combine like terms: 7414559.985 + -7414559.985 = 0.000 0.000 + -9796.263151x + x2 = 0 + -7414559.985 -9796.263151x + x2 = 0 + -7414559.985 Combine like terms: 0 + -7414559.985 = -7414559.985 -9796.263151x + x2 = -7414559.985 The x term is -9796.263151x. Take half its coefficient (-4898.131576). Square it (23991692.94) and add it to both sides. Add '23991692.94' to each side of the equation. -9796.263151x + 23991692.94 + x2 = -7414559.985 + 23991692.94 Reorder the terms: 23991692.94 + -9796.263151x + x2 = -7414559.985 + 23991692.94 Combine like terms: -7414559.985 + 23991692.94 = 16577132.955 23991692.94 + -9796.263151x + x2 = 16577132.955 Factor a perfect square on the left side: (x + -4898.131576)(x + -4898.131576) = 16577132.955 Calculate the square root of the right side: 4071.502542674 Break this problem into two subproblems by setting (x + -4898.131576) equal to 4071.502542674 and -4071.502542674.Subproblem 1
x + -4898.131576 = 4071.502542674 Simplifying x + -4898.131576 = 4071.502542674 Reorder the terms: -4898.131576 + x = 4071.502542674 Solving -4898.131576 + x = 4071.502542674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4898.131576' to each side of the equation. -4898.131576 + 4898.131576 + x = 4071.502542674 + 4898.131576 Combine like terms: -4898.131576 + 4898.131576 = 0.000000 0.000000 + x = 4071.502542674 + 4898.131576 x = 4071.502542674 + 4898.131576 Combine like terms: 4071.502542674 + 4898.131576 = 8969.634118674 x = 8969.634118674 Simplifying x = 8969.634118674Subproblem 2
x + -4898.131576 = -4071.502542674 Simplifying x + -4898.131576 = -4071.502542674 Reorder the terms: -4898.131576 + x = -4071.502542674 Solving -4898.131576 + x = -4071.502542674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4898.131576' to each side of the equation. -4898.131576 + 4898.131576 + x = -4071.502542674 + 4898.131576 Combine like terms: -4898.131576 + 4898.131576 = 0.000000 0.000000 + x = -4071.502542674 + 4898.131576 x = -4071.502542674 + 4898.131576 Combine like terms: -4071.502542674 + 4898.131576 = 826.629033326 x = 826.629033326 Simplifying x = 826.629033326Solution
The solution to the problem is based on the solutions from the subproblems. x = {8969.634118674, 826.629033326}
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