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Simplifying 4x + -101(3x2 + -15) = 0 Reorder the terms: 4x + -101(-15 + 3x2) = 0 4x + (-15 * -101 + 3x2 * -101) = 0 4x + (1515 + -303x2) = 0 Reorder the terms: 1515 + 4x + -303x2 = 0 Solving 1515 + 4x + -303x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -303 the coefficient of the squared term: Divide each side by '-303'. -5 + -0.01320132013x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.01320132013x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.01320132013x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.01320132013x + x2 = 0 + 5 -0.01320132013x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.01320132013x + x2 = 5 The x term is -0.01320132013x. Take half its coefficient (-0.006600660065). Square it (0.00004356871329) and add it to both sides. Add '0.00004356871329' to each side of the equation. -0.01320132013x + 0.00004356871329 + x2 = 5 + 0.00004356871329 Reorder the terms: 0.00004356871329 + -0.01320132013x + x2 = 5 + 0.00004356871329 Combine like terms: 5 + 0.00004356871329 = 5.00004356871329 0.00004356871329 + -0.01320132013x + x2 = 5.00004356871329 Factor a perfect square on the left side: (x + -0.006600660065)(x + -0.006600660065) = 5.00004356871329 Calculate the square root of the right side: 2.23607772 Break this problem into two subproblems by setting (x + -0.006600660065) equal to 2.23607772 and -2.23607772.Subproblem 1
x + -0.006600660065 = 2.23607772 Simplifying x + -0.006600660065 = 2.23607772 Reorder the terms: -0.006600660065 + x = 2.23607772 Solving -0.006600660065 + x = 2.23607772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006600660065' to each side of the equation. -0.006600660065 + 0.006600660065 + x = 2.23607772 + 0.006600660065 Combine like terms: -0.006600660065 + 0.006600660065 = 0.000000000000 0.000000000000 + x = 2.23607772 + 0.006600660065 x = 2.23607772 + 0.006600660065 Combine like terms: 2.23607772 + 0.006600660065 = 2.242678380065 x = 2.242678380065 Simplifying x = 2.242678380065Subproblem 2
x + -0.006600660065 = -2.23607772 Simplifying x + -0.006600660065 = -2.23607772 Reorder the terms: -0.006600660065 + x = -2.23607772 Solving -0.006600660065 + x = -2.23607772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006600660065' to each side of the equation. -0.006600660065 + 0.006600660065 + x = -2.23607772 + 0.006600660065 Combine like terms: -0.006600660065 + 0.006600660065 = 0.000000000000 0.000000000000 + x = -2.23607772 + 0.006600660065 x = -2.23607772 + 0.006600660065 Combine like terms: -2.23607772 + 0.006600660065 = -2.229477059935 x = -2.229477059935 Simplifying x = -2.229477059935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.242678380065, -2.229477059935}
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