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Simplifying 670x2 + -48x + -69517000 = 0 Reorder the terms: -69517000 + -48x + 670x2 = 0 Solving -69517000 + -48x + 670x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-34758500 + -24x + 335x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-34758500 + -24x + 335x2)' equal to zero and attempt to solve: Simplifying -34758500 + -24x + 335x2 = 0 Solving -34758500 + -24x + 335x2 = 0 Begin completing the square. Divide all terms by 335 the coefficient of the squared term: Divide each side by '335'. -103756.7164 + -0.07164179104x + x2 = 0 Move the constant term to the right: Add '103756.7164' to each side of the equation. -103756.7164 + -0.07164179104x + 103756.7164 + x2 = 0 + 103756.7164 Reorder the terms: -103756.7164 + 103756.7164 + -0.07164179104x + x2 = 0 + 103756.7164 Combine like terms: -103756.7164 + 103756.7164 = 0.0000 0.0000 + -0.07164179104x + x2 = 0 + 103756.7164 -0.07164179104x + x2 = 0 + 103756.7164 Combine like terms: 0 + 103756.7164 = 103756.7164 -0.07164179104x + x2 = 103756.7164 The x term is -0.07164179104x. Take half its coefficient (-0.03582089552). Square it (0.001283136556) and add it to both sides. Add '0.001283136556' to each side of the equation. -0.07164179104x + 0.001283136556 + x2 = 103756.7164 + 0.001283136556 Reorder the terms: 0.001283136556 + -0.07164179104x + x2 = 103756.7164 + 0.001283136556 Combine like terms: 103756.7164 + 0.001283136556 = 103756.717683136556 0.001283136556 + -0.07164179104x + x2 = 103756.717683136556 Factor a perfect square on the left side: (x + -0.03582089552)(x + -0.03582089552) = 103756.717683136556 Calculate the square root of the right side: 322.112895866 Break this problem into two subproblems by setting (x + -0.03582089552) equal to 322.112895866 and -322.112895866.Subproblem 1
x + -0.03582089552 = 322.112895866 Simplifying x + -0.03582089552 = 322.112895866 Reorder the terms: -0.03582089552 + x = 322.112895866 Solving -0.03582089552 + x = 322.112895866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03582089552' to each side of the equation. -0.03582089552 + 0.03582089552 + x = 322.112895866 + 0.03582089552 Combine like terms: -0.03582089552 + 0.03582089552 = 0.00000000000 0.00000000000 + x = 322.112895866 + 0.03582089552 x = 322.112895866 + 0.03582089552 Combine like terms: 322.112895866 + 0.03582089552 = 322.14871676152 x = 322.14871676152 Simplifying x = 322.14871676152Subproblem 2
x + -0.03582089552 = -322.112895866 Simplifying x + -0.03582089552 = -322.112895866 Reorder the terms: -0.03582089552 + x = -322.112895866 Solving -0.03582089552 + x = -322.112895866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03582089552' to each side of the equation. -0.03582089552 + 0.03582089552 + x = -322.112895866 + 0.03582089552 Combine like terms: -0.03582089552 + 0.03582089552 = 0.00000000000 0.00000000000 + x = -322.112895866 + 0.03582089552 x = -322.112895866 + 0.03582089552 Combine like terms: -322.112895866 + 0.03582089552 = -322.07707497048 x = -322.07707497048 Simplifying x = -322.07707497048Solution
The solution to the problem is based on the solutions from the subproblems. x = {322.14871676152, -322.07707497048}Solution
x = {322.14871676152, -322.07707497048}
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