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Simplifying 3x2 + -64x + 252 = 0 Reorder the terms: 252 + -64x + 3x2 = 0 Solving 252 + -64x + 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'. 84 + -21.33333333x + x2 = 0 Move the constant term to the right: Add '-84' to each side of the equation. 84 + -21.33333333x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + -21.33333333x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + -21.33333333x + x2 = 0 + -84 -21.33333333x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 -21.33333333x + x2 = -84 The x term is -21.33333333x. Take half its coefficient (-10.66666667). Square it (113.7777778) and add it to both sides. Add '113.7777778' to each side of the equation. -21.33333333x + 113.7777778 + x2 = -84 + 113.7777778 Reorder the terms: 113.7777778 + -21.33333333x + x2 = -84 + 113.7777778 Combine like terms: -84 + 113.7777778 = 29.7777778 113.7777778 + -21.33333333x + x2 = 29.7777778 Factor a perfect square on the left side: (x + -10.66666667)(x + -10.66666667) = 29.7777778 Calculate the square root of the right side: 5.45690185 Break this problem into two subproblems by setting (x + -10.66666667) equal to 5.45690185 and -5.45690185.Subproblem 1
x + -10.66666667 = 5.45690185 Simplifying x + -10.66666667 = 5.45690185 Reorder the terms: -10.66666667 + x = 5.45690185 Solving -10.66666667 + x = 5.45690185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.66666667' to each side of the equation. -10.66666667 + 10.66666667 + x = 5.45690185 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + x = 5.45690185 + 10.66666667 x = 5.45690185 + 10.66666667 Combine like terms: 5.45690185 + 10.66666667 = 16.12356852 x = 16.12356852 Simplifying x = 16.12356852Subproblem 2
x + -10.66666667 = -5.45690185 Simplifying x + -10.66666667 = -5.45690185 Reorder the terms: -10.66666667 + x = -5.45690185 Solving -10.66666667 + x = -5.45690185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.66666667' to each side of the equation. -10.66666667 + 10.66666667 + x = -5.45690185 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + x = -5.45690185 + 10.66666667 x = -5.45690185 + 10.66666667 Combine like terms: -5.45690185 + 10.66666667 = 5.20976482 x = 5.20976482 Simplifying x = 5.20976482Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.12356852, 5.20976482}
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