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Simplifying 3x2 + 5x + 20 = 100x + -2 Reorder the terms: 20 + 5x + 3x2 = 100x + -2 Reorder the terms: 20 + 5x + 3x2 = -2 + 100x Solving 20 + 5x + 3x2 = -2 + 100x Solving for variable 'x'. Reorder the terms: 20 + 2 + 5x + -100x + 3x2 = -2 + 100x + 2 + -100x Combine like terms: 20 + 2 = 22 22 + 5x + -100x + 3x2 = -2 + 100x + 2 + -100x Combine like terms: 5x + -100x = -95x 22 + -95x + 3x2 = -2 + 100x + 2 + -100x Reorder the terms: 22 + -95x + 3x2 = -2 + 2 + 100x + -100x Combine like terms: -2 + 2 = 0 22 + -95x + 3x2 = 0 + 100x + -100x 22 + -95x + 3x2 = 100x + -100x Combine like terms: 100x + -100x = 0 22 + -95x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.333333333 + -31.66666667x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -31.66666667x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -31.66666667x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -31.66666667x + x2 = 0 + -7.333333333 -31.66666667x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -31.66666667x + x2 = -7.333333333 The x term is -31.66666667x. Take half its coefficient (-15.83333334). Square it (250.6944447) and add it to both sides. Add '250.6944447' to each side of the equation. -31.66666667x + 250.6944447 + x2 = -7.333333333 + 250.6944447 Reorder the terms: 250.6944447 + -31.66666667x + x2 = -7.333333333 + 250.6944447 Combine like terms: -7.333333333 + 250.6944447 = 243.361111367 250.6944447 + -31.66666667x + x2 = 243.361111367 Factor a perfect square on the left side: (x + -15.83333334)(x + -15.83333334) = 243.361111367 Calculate the square root of the right side: 15.600035621 Break this problem into two subproblems by setting (x + -15.83333334) equal to 15.600035621 and -15.600035621.Subproblem 1
x + -15.83333334 = 15.600035621 Simplifying x + -15.83333334 = 15.600035621 Reorder the terms: -15.83333334 + x = 15.600035621 Solving -15.83333334 + x = 15.600035621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.83333334' to each side of the equation. -15.83333334 + 15.83333334 + x = 15.600035621 + 15.83333334 Combine like terms: -15.83333334 + 15.83333334 = 0.00000000 0.00000000 + x = 15.600035621 + 15.83333334 x = 15.600035621 + 15.83333334 Combine like terms: 15.600035621 + 15.83333334 = 31.433368961 x = 31.433368961 Simplifying x = 31.433368961Subproblem 2
x + -15.83333334 = -15.600035621 Simplifying x + -15.83333334 = -15.600035621 Reorder the terms: -15.83333334 + x = -15.600035621 Solving -15.83333334 + x = -15.600035621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.83333334' to each side of the equation. -15.83333334 + 15.83333334 + x = -15.600035621 + 15.83333334 Combine like terms: -15.83333334 + 15.83333334 = 0.00000000 0.00000000 + x = -15.600035621 + 15.83333334 x = -15.600035621 + 15.83333334 Combine like terms: -15.600035621 + 15.83333334 = 0.233297719 x = 0.233297719 Simplifying x = 0.233297719Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.433368961, 0.233297719}
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