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Simplifying 6(x2 + -10x + 25) = 1 Reorder the terms: 6(25 + -10x + x2) = 1 (25 * 6 + -10x * 6 + x2 * 6) = 1 (150 + -60x + 6x2) = 1 Solving 150 + -60x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: 150 + -1 + -60x + 6x2 = 1 + -1 Combine like terms: 150 + -1 = 149 149 + -60x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 149 + -60x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 24.83333333 + -10x + x2 = 0 Move the constant term to the right: Add '-24.83333333' to each side of the equation. 24.83333333 + -10x + -24.83333333 + x2 = 0 + -24.83333333 Reorder the terms: 24.83333333 + -24.83333333 + -10x + x2 = 0 + -24.83333333 Combine like terms: 24.83333333 + -24.83333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -24.83333333 -10x + x2 = 0 + -24.83333333 Combine like terms: 0 + -24.83333333 = -24.83333333 -10x + x2 = -24.83333333 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 = -24.83333333 + 25 Reorder the terms: 25 + -10x + x2 = -24.83333333 + 25 Combine like terms: -24.83333333 + 25 = 0.16666667 25 + -10x + x2 = 0.16666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 0.16666667 Calculate the square root of the right side: 0.408248295 Break this problem into two subproblems by setting (x + -5) equal to 0.408248295 and -0.408248295.Subproblem 1
x + -5 = 0.408248295 Simplifying x + -5 = 0.408248295 Reorder the terms: -5 + x = 0.408248295 Solving -5 + x = 0.408248295 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 = 0.408248295 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0.408248295 + 5 x = 0.408248295 + 5 Combine like terms: 0.408248295 + 5 = 5.408248295 x = 5.408248295 Simplifying x = 5.408248295Subproblem 2
x + -5 = -0.408248295 Simplifying x + -5 = -0.408248295 Reorder the terms: -5 + x = -0.408248295 Solving -5 + x = -0.408248295 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 = -0.408248295 + 5 Combine like terms: -5 + 5 = 0 0 + x = -0.408248295 + 5 x = -0.408248295 + 5 Combine like terms: -0.408248295 + 5 = 4.591751705 x = 4.591751705 Simplifying x = 4.591751705Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.408248295, 4.591751705}
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