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Simplifying 39x2 + -474x + -2460 = 0 Reorder the terms: -2460 + -474x + 39x2 = 0 Solving -2460 + -474x + 39x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-820 + -158x + 13x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-820 + -158x + 13x2)' equal to zero and attempt to solve: Simplifying -820 + -158x + 13x2 = 0 Solving -820 + -158x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -63.07692308 + -12.15384615x + x2 = 0 Move the constant term to the right: Add '63.07692308' to each side of the equation. -63.07692308 + -12.15384615x + 63.07692308 + x2 = 0 + 63.07692308 Reorder the terms: -63.07692308 + 63.07692308 + -12.15384615x + x2 = 0 + 63.07692308 Combine like terms: -63.07692308 + 63.07692308 = 0.00000000 0.00000000 + -12.15384615x + x2 = 0 + 63.07692308 -12.15384615x + x2 = 0 + 63.07692308 Combine like terms: 0 + 63.07692308 = 63.07692308 -12.15384615x + x2 = 63.07692308 The x term is -12.15384615x. Take half its coefficient (-6.076923075). Square it (36.92899406) and add it to both sides. Add '36.92899406' to each side of the equation. -12.15384615x + 36.92899406 + x2 = 63.07692308 + 36.92899406 Reorder the terms: 36.92899406 + -12.15384615x + x2 = 63.07692308 + 36.92899406 Combine like terms: 63.07692308 + 36.92899406 = 100.00591714 36.92899406 + -12.15384615x + x2 = 100.00591714 Factor a perfect square on the left side: (x + -6.076923075)(x + -6.076923075) = 100.00591714 Calculate the square root of the right side: 10.000295853 Break this problem into two subproblems by setting (x + -6.076923075) equal to 10.000295853 and -10.000295853.Subproblem 1
x + -6.076923075 = 10.000295853 Simplifying x + -6.076923075 = 10.000295853 Reorder the terms: -6.076923075 + x = 10.000295853 Solving -6.076923075 + x = 10.000295853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.076923075' to each side of the equation. -6.076923075 + 6.076923075 + x = 10.000295853 + 6.076923075 Combine like terms: -6.076923075 + 6.076923075 = 0.000000000 0.000000000 + x = 10.000295853 + 6.076923075 x = 10.000295853 + 6.076923075 Combine like terms: 10.000295853 + 6.076923075 = 16.077218928 x = 16.077218928 Simplifying x = 16.077218928Subproblem 2
x + -6.076923075 = -10.000295853 Simplifying x + -6.076923075 = -10.000295853 Reorder the terms: -6.076923075 + x = -10.000295853 Solving -6.076923075 + x = -10.000295853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.076923075' to each side of the equation. -6.076923075 + 6.076923075 + x = -10.000295853 + 6.076923075 Combine like terms: -6.076923075 + 6.076923075 = 0.000000000 0.000000000 + x = -10.000295853 + 6.076923075 x = -10.000295853 + 6.076923075 Combine like terms: -10.000295853 + 6.076923075 = -3.923372778 x = -3.923372778 Simplifying x = -3.923372778Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.077218928, -3.923372778}Solution
x = {16.077218928, -3.923372778}
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