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Simplifying 2x * 3x = 10(10x + 10) Reorder the terms for easier multiplication: 2 * 3x * x = 10(10x + 10) Multiply 2 * 3 6x * x = 10(10x + 10) Multiply x * x 6x2 = 10(10x + 10) Reorder the terms: 6x2 = 10(10 + 10x) 6x2 = (10 * 10 + 10x * 10) 6x2 = (100 + 100x) Solving 6x2 = 100 + 100x Solving for variable 'x'. Reorder the terms: -100 + -100x + 6x2 = 100 + 100x + -100 + -100x Reorder the terms: -100 + -100x + 6x2 = 100 + -100 + 100x + -100x Combine like terms: 100 + -100 = 0 -100 + -100x + 6x2 = 0 + 100x + -100x -100 + -100x + 6x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -100 + -100x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -50x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + -50x + 3x2)' equal to zero and attempt to solve: Simplifying -50 + -50x + 3x2 = 0 Solving -50 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -16.66666667x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -16.66666667x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -16.66666667x + x2 = 0 + 16.66666667 -16.66666667x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -16.66666667x + x2 = 16.66666667 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = 16.66666667 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 16.66666667 + 69.44444447 Combine like terms: 16.66666667 + 69.44444447 = 86.11111114 69.44444447 + -16.66666667x + x2 = 86.11111114 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 86.11111114 Calculate the square root of the right side: 9.279607273 Break this problem into two subproblems by setting (x + -8.333333335) equal to 9.279607273 and -9.279607273.Subproblem 1
x + -8.333333335 = 9.279607273 Simplifying x + -8.333333335 = 9.279607273 Reorder the terms: -8.333333335 + x = 9.279607273 Solving -8.333333335 + x = 9.279607273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 9.279607273 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 9.279607273 + 8.333333335 x = 9.279607273 + 8.333333335 Combine like terms: 9.279607273 + 8.333333335 = 17.612940608 x = 17.612940608 Simplifying x = 17.612940608Subproblem 2
x + -8.333333335 = -9.279607273 Simplifying x + -8.333333335 = -9.279607273 Reorder the terms: -8.333333335 + x = -9.279607273 Solving -8.333333335 + x = -9.279607273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -9.279607273 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -9.279607273 + 8.333333335 x = -9.279607273 + 8.333333335 Combine like terms: -9.279607273 + 8.333333335 = -0.946273938 x = -0.946273938 Simplifying x = -0.946273938Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.612940608, -0.946273938}Solution
x = {17.612940608, -0.946273938}
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