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Simplifying 2x + 1 + -3x + 5 = 3x(x + 10) Reorder the terms: 1 + 5 + 2x + -3x = 3x(x + 10) Combine like terms: 1 + 5 = 6 6 + 2x + -3x = 3x(x + 10) Combine like terms: 2x + -3x = -1x 6 + -1x = 3x(x + 10) Reorder the terms: 6 + -1x = 3x(10 + x) 6 + -1x = (10 * 3x + x * 3x) 6 + -1x = (30x + 3x2) Solving 6 + -1x = 30x + 3x2 Solving for variable 'x'. Combine like terms: -1x + -30x = -31x 6 + -31x + -3x2 = 30x + 3x2 + -30x + -3x2 Reorder the terms: 6 + -31x + -3x2 = 30x + -30x + 3x2 + -3x2 Combine like terms: 30x + -30x = 0 6 + -31x + -3x2 = 0 + 3x2 + -3x2 6 + -31x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 6 + -31x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + 10.33333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 10.33333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 10.33333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10.33333333x + x2 = 0 + 2 10.33333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 10.33333333x + x2 = 2 The x term is 10.33333333x. Take half its coefficient (5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. 10.33333333x + 26.69444443 + x2 = 2 + 26.69444443 Reorder the terms: 26.69444443 + 10.33333333x + x2 = 2 + 26.69444443 Combine like terms: 2 + 26.69444443 = 28.69444443 26.69444443 + 10.33333333x + x2 = 28.69444443 Factor a perfect square on the left side: (x + 5.166666665)(x + 5.166666665) = 28.69444443 Calculate the square root of the right side: 5.356719559 Break this problem into two subproblems by setting (x + 5.166666665) equal to 5.356719559 and -5.356719559.Subproblem 1
x + 5.166666665 = 5.356719559 Simplifying x + 5.166666665 = 5.356719559 Reorder the terms: 5.166666665 + x = 5.356719559 Solving 5.166666665 + x = 5.356719559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = 5.356719559 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = 5.356719559 + -5.166666665 x = 5.356719559 + -5.166666665 Combine like terms: 5.356719559 + -5.166666665 = 0.190052894 x = 0.190052894 Simplifying x = 0.190052894Subproblem 2
x + 5.166666665 = -5.356719559 Simplifying x + 5.166666665 = -5.356719559 Reorder the terms: 5.166666665 + x = -5.356719559 Solving 5.166666665 + x = -5.356719559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = -5.356719559 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = -5.356719559 + -5.166666665 x = -5.356719559 + -5.166666665 Combine like terms: -5.356719559 + -5.166666665 = -10.523386224 x = -10.523386224 Simplifying x = -10.523386224Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.190052894, -10.523386224}
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