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Simplifying x2 + -56x + 167 = 43 Reorder the terms: 167 + -56x + x2 = 43 Solving 167 + -56x + x2 = 43 Solving for variable 'x'. Reorder the terms: 167 + -43 + -56x + x2 = 43 + -43 Combine like terms: 167 + -43 = 124 124 + -56x + x2 = 43 + -43 Combine like terms: 43 + -43 = 0 124 + -56x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -56x + -124 + x2 = 0 + -124 Reorder the terms: 124 + -124 + -56x + x2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -56x + x2 = 0 + -124 -56x + x2 = 0 + -124 Combine like terms: 0 + -124 = -124 -56x + x2 = -124 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = -124 + 784 Reorder the terms: 784 + -56x + x2 = -124 + 784 Combine like terms: -124 + 784 = 660 784 + -56x + x2 = 660 Factor a perfect square on the left side: (x + -28)(x + -28) = 660 Calculate the square root of the right side: 25.690465157 Break this problem into two subproblems by setting (x + -28) equal to 25.690465157 and -25.690465157.Subproblem 1
x + -28 = 25.690465157 Simplifying x + -28 = 25.690465157 Reorder the terms: -28 + x = 25.690465157 Solving -28 + x = 25.690465157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 25.690465157 + 28 Combine like terms: -28 + 28 = 0 0 + x = 25.690465157 + 28 x = 25.690465157 + 28 Combine like terms: 25.690465157 + 28 = 53.690465157 x = 53.690465157 Simplifying x = 53.690465157Subproblem 2
x + -28 = -25.690465157 Simplifying x + -28 = -25.690465157 Reorder the terms: -28 + x = -25.690465157 Solving -28 + x = -25.690465157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -25.690465157 + 28 Combine like terms: -28 + 28 = 0 0 + x = -25.690465157 + 28 x = -25.690465157 + 28 Combine like terms: -25.690465157 + 28 = 2.309534843 x = 2.309534843 Simplifying x = 2.309534843Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.690465157, 2.309534843}
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