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Simplifying x2 + -10x + -56 = 6 Reorder the terms: -56 + -10x + x2 = 6 Solving -56 + -10x + x2 = 6 Solving for variable 'x'. Reorder the terms: -56 + -6 + -10x + x2 = 6 + -6 Combine like terms: -56 + -6 = -62 -62 + -10x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -62 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + -10x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + -10x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + -10x + x2 = 0 + 62 -10x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 -10x + x2 = 62 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 = 62 + 25 Reorder the terms: 25 + -10x + x2 = 62 + 25 Combine like terms: 62 + 25 = 87 25 + -10x + x2 = 87 Factor a perfect square on the left side: (x + -5)(x + -5) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + -5) equal to 9.327379053 and -9.327379053.Subproblem 1
x + -5 = 9.327379053 Simplifying x + -5 = 9.327379053 Reorder the terms: -5 + x = 9.327379053 Solving -5 + x = 9.327379053 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 = 9.327379053 + 5 Combine like terms: -5 + 5 = 0 0 + x = 9.327379053 + 5 x = 9.327379053 + 5 Combine like terms: 9.327379053 + 5 = 14.327379053 x = 14.327379053 Simplifying x = 14.327379053Subproblem 2
x + -5 = -9.327379053 Simplifying x + -5 = -9.327379053 Reorder the terms: -5 + x = -9.327379053 Solving -5 + x = -9.327379053 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 = -9.327379053 + 5 Combine like terms: -5 + 5 = 0 0 + x = -9.327379053 + 5 x = -9.327379053 + 5 Combine like terms: -9.327379053 + 5 = -4.327379053 x = -4.327379053 Simplifying x = -4.327379053Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.327379053, -4.327379053}
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