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Simplifying 14x(3x + 10) = 360 Reorder the terms: 14x(10 + 3x) = 360 (10 * 14x + 3x * 14x) = 360 (140x + 42x2) = 360 Solving 140x + 42x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 140x + 42x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 140x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-180 + 70x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-180 + 70x + 21x2)' equal to zero and attempt to solve: Simplifying -180 + 70x + 21x2 = 0 Solving -180 + 70x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -8.571428571 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + 3.333333333x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + 3.333333333x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + 8.571428571 3.333333333x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 3.333333333x + x2 = 8.571428571 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 8.571428571 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 8.571428571 + 2.777777779 Combine like terms: 8.571428571 + 2.777777779 = 11.34920635 2.777777779 + 3.333333333x + x2 = 11.34920635 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 11.34920635 Calculate the square root of the right side: 3.368858316 Break this problem into two subproblems by setting (x + 1.666666667) equal to 3.368858316 and -3.368858316.Subproblem 1
x + 1.666666667 = 3.368858316 Simplifying x + 1.666666667 = 3.368858316 Reorder the terms: 1.666666667 + x = 3.368858316 Solving 1.666666667 + x = 3.368858316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 3.368858316 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.368858316 + -1.666666667 x = 3.368858316 + -1.666666667 Combine like terms: 3.368858316 + -1.666666667 = 1.702191649 x = 1.702191649 Simplifying x = 1.702191649Subproblem 2
x + 1.666666667 = -3.368858316 Simplifying x + 1.666666667 = -3.368858316 Reorder the terms: 1.666666667 + x = -3.368858316 Solving 1.666666667 + x = -3.368858316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -3.368858316 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.368858316 + -1.666666667 x = -3.368858316 + -1.666666667 Combine like terms: -3.368858316 + -1.666666667 = -5.035524983 x = -5.035524983 Simplifying x = -5.035524983Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.702191649, -5.035524983}Solution
x = {1.702191649, -5.035524983}
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