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Simplifying (x)(3x + -3) = 50 Reorder the terms: x(-3 + 3x) = 50 (-3 * x + 3x * x) = 50 (-3x + 3x2) = 50 Solving -3x + 3x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -3x + 3x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.66666667 + -1x + x2 = 0 Move the constant term to the right: Add '16.66666667' to each side of the equation. -16.66666667 + -1x + 16.66666667 + x2 = 0 + 16.66666667 Reorder the terms: -16.66666667 + 16.66666667 + -1x + x2 = 0 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + -1x + x2 = 0 + 16.66666667 -1x + x2 = 0 + 16.66666667 Combine like terms: 0 + 16.66666667 = 16.66666667 -1x + x2 = 16.66666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 16.66666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 16.66666667 + 0.25 Combine like terms: 16.66666667 + 0.25 = 16.91666667 0.25 + -1x + x2 = 16.91666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 16.91666667 Calculate the square root of the right side: 4.11298756 Break this problem into two subproblems by setting (x + -0.5) equal to 4.11298756 and -4.11298756.Subproblem 1
x + -0.5 = 4.11298756 Simplifying x + -0.5 = 4.11298756 Reorder the terms: -0.5 + x = 4.11298756 Solving -0.5 + x = 4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.11298756 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.11298756 + 0.5 x = 4.11298756 + 0.5 Combine like terms: 4.11298756 + 0.5 = 4.61298756 x = 4.61298756 Simplifying x = 4.61298756Subproblem 2
x + -0.5 = -4.11298756 Simplifying x + -0.5 = -4.11298756 Reorder the terms: -0.5 + x = -4.11298756 Solving -0.5 + x = -4.11298756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.11298756 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.11298756 + 0.5 x = -4.11298756 + 0.5 Combine like terms: -4.11298756 + 0.5 = -3.61298756 x = -3.61298756 Simplifying x = -3.61298756Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.61298756, -3.61298756}
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