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Simplifying 6x2 = 30x + -22 Reorder the terms: 6x2 = -22 + 30x Solving 6x2 = -22 + 30x Solving for variable 'x'. Reorder the terms: 22 + -30x + 6x2 = -22 + 30x + 22 + -30x Reorder the terms: 22 + -30x + 6x2 = -22 + 22 + 30x + -30x Combine like terms: -22 + 22 = 0 22 + -30x + 6x2 = 0 + 30x + -30x 22 + -30x + 6x2 = 30x + -30x Combine like terms: 30x + -30x = 0 22 + -30x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying 11 + -15x + 3x2 = 0 Solving 11 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + -5x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + -5x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + -3.666666667 -5x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 -5x + x2 = -3.666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.666666667 + 6.25 Combine like terms: -3.666666667 + 6.25 = 2.583333333 6.25 + -5x + x2 = 2.583333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (x + -2.5) equal to 1.607275127 and -1.607275127.Subproblem 1
x + -2.5 = 1.607275127 Simplifying x + -2.5 = 1.607275127 Reorder the terms: -2.5 + x = 1.607275127 Solving -2.5 + x = 1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.607275127 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.607275127 + 2.5 x = 1.607275127 + 2.5 Combine like terms: 1.607275127 + 2.5 = 4.107275127 x = 4.107275127 Simplifying x = 4.107275127Subproblem 2
x + -2.5 = -1.607275127 Simplifying x + -2.5 = -1.607275127 Reorder the terms: -2.5 + x = -1.607275127 Solving -2.5 + x = -1.607275127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.607275127 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.607275127 + 2.5 x = -1.607275127 + 2.5 Combine like terms: -1.607275127 + 2.5 = 0.892724873 x = 0.892724873 Simplifying x = 0.892724873Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.107275127, 0.892724873}Solution
x = {4.107275127, 0.892724873}
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