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Simplifying 6x2 + 12x = 230 Reorder the terms: 12x + 6x2 = 230 Solving 12x + 6x2 = 230 Solving for variable 'x'. Reorder the terms: -230 + 12x + 6x2 = 230 + -230 Combine like terms: 230 + -230 = 0 -230 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-115 + 6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-115 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -115 + 6x + 3x2 = 0 Solving -115 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -38.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '38.33333333' to each side of the equation. -38.33333333 + 2x + 38.33333333 + x2 = 0 + 38.33333333 Reorder the terms: -38.33333333 + 38.33333333 + 2x + x2 = 0 + 38.33333333 Combine like terms: -38.33333333 + 38.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 38.33333333 2x + x2 = 0 + 38.33333333 Combine like terms: 0 + 38.33333333 = 38.33333333 2x + x2 = 38.33333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 38.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 38.33333333 + 1 Combine like terms: 38.33333333 + 1 = 39.33333333 1 + 2x + x2 = 39.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 39.33333333 Calculate the square root of the right side: 6.27162924 Break this problem into two subproblems by setting (x + 1) equal to 6.27162924 and -6.27162924.Subproblem 1
x + 1 = 6.27162924 Simplifying x + 1 = 6.27162924 Reorder the terms: 1 + x = 6.27162924 Solving 1 + x = 6.27162924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.27162924 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.27162924 + -1 x = 6.27162924 + -1 Combine like terms: 6.27162924 + -1 = 5.27162924 x = 5.27162924 Simplifying x = 5.27162924Subproblem 2
x + 1 = -6.27162924 Simplifying x + 1 = -6.27162924 Reorder the terms: 1 + x = -6.27162924 Solving 1 + x = -6.27162924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.27162924 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.27162924 + -1 x = -6.27162924 + -1 Combine like terms: -6.27162924 + -1 = -7.27162924 x = -7.27162924 Simplifying x = -7.27162924Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.27162924, -7.27162924}Solution
x = {5.27162924, -7.27162924}
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