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Simplifying x2 + -6x + 9 * 4x + -1x * 4x + -5 = 0 Multiply 9 * 4 x2 + -6x + 36x + -1x * 4x + -5 = 0 Reorder the terms for easier multiplication: x2 + -6x + 36x + -1 * 4x * x + -5 = 0 Multiply -1 * 4 x2 + -6x + 36x + -4x * x + -5 = 0 Multiply x * x x2 + -6x + 36x + -4x2 + -5 = 0 Reorder the terms: -5 + -6x + 36x + x2 + -4x2 = 0 Combine like terms: -6x + 36x = 30x -5 + 30x + x2 + -4x2 = 0 Combine like terms: x2 + -4x2 = -3x2 -5 + 30x + -3x2 = 0 Solving -5 + 30x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -10x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -10x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -10x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -10x + x2 = 0 + -1.666666667 -10x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -10x + x2 = -1.666666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -1.666666667 + 25 Reorder the terms: 25 + -10x + x2 = -1.666666667 + 25 Combine like terms: -1.666666667 + 25 = 23.333333333 25 + -10x + x2 = 23.333333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 23.333333333 Calculate the square root of the right side: 4.830458915 Break this problem into two subproblems by setting (x + -5) equal to 4.830458915 and -4.830458915.Subproblem 1
x + -5 = 4.830458915 Simplifying x + -5 = 4.830458915 Reorder the terms: -5 + x = 4.830458915 Solving -5 + x = 4.830458915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.830458915 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.830458915 + 5 x = 4.830458915 + 5 Combine like terms: 4.830458915 + 5 = 9.830458915 x = 9.830458915 Simplifying x = 9.830458915Subproblem 2
x + -5 = -4.830458915 Simplifying x + -5 = -4.830458915 Reorder the terms: -5 + x = -4.830458915 Solving -5 + x = -4.830458915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.830458915 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.830458915 + 5 x = -4.830458915 + 5 Combine like terms: -4.830458915 + 5 = 0.169541085 x = 0.169541085 Simplifying x = 0.169541085Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.830458915, 0.169541085}
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