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Simplifying x2 + -112x + 36 = 0 Reorder the terms: 36 + -112x + x2 = 0 Solving 36 + -112x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -112x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -112x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -112x + x2 = 0 + -36 -112x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -112x + x2 = -36 The x term is -112x. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112x + 3136 + x2 = -36 + 3136 Reorder the terms: 3136 + -112x + x2 = -36 + 3136 Combine like terms: -36 + 3136 = 3100 3136 + -112x + x2 = 3100 Factor a perfect square on the left side: (x + -56)(x + -56) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + -56) equal to 55.677643628 and -55.677643628.Subproblem 1
x + -56 = 55.677643628 Simplifying x + -56 = 55.677643628 Reorder the terms: -56 + x = 55.677643628 Solving -56 + x = 55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = 55.677643628 + 56 Combine like terms: -56 + 56 = 0 0 + x = 55.677643628 + 56 x = 55.677643628 + 56 Combine like terms: 55.677643628 + 56 = 111.677643628 x = 111.677643628 Simplifying x = 111.677643628Subproblem 2
x + -56 = -55.677643628 Simplifying x + -56 = -55.677643628 Reorder the terms: -56 + x = -55.677643628 Solving -56 + x = -55.677643628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = -55.677643628 + 56 Combine like terms: -56 + 56 = 0 0 + x = -55.677643628 + 56 x = -55.677643628 + 56 Combine like terms: -55.677643628 + 56 = 0.322356372 x = 0.322356372 Simplifying x = 0.322356372Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.677643628, 0.322356372}
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