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Simplifying x2 + -42x + 153 = 0 Reorder the terms: 153 + -42x + x2 = 0 Solving 153 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-153' to each side of the equation. 153 + -42x + -153 + x2 = 0 + -153 Reorder the terms: 153 + -153 + -42x + x2 = 0 + -153 Combine like terms: 153 + -153 = 0 0 + -42x + x2 = 0 + -153 -42x + x2 = 0 + -153 Combine like terms: 0 + -153 = -153 -42x + x2 = -153 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -153 + 441 Reorder the terms: 441 + -42x + x2 = -153 + 441 Combine like terms: -153 + 441 = 288 441 + -42x + x2 = 288 Factor a perfect square on the left side: (x + -21)(x + -21) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (x + -21) equal to 16.970562748 and -16.970562748.Subproblem 1
x + -21 = 16.970562748 Simplifying x + -21 = 16.970562748 Reorder the terms: -21 + x = 16.970562748 Solving -21 + x = 16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 16.970562748 + 21 Combine like terms: -21 + 21 = 0 0 + x = 16.970562748 + 21 x = 16.970562748 + 21 Combine like terms: 16.970562748 + 21 = 37.970562748 x = 37.970562748 Simplifying x = 37.970562748Subproblem 2
x + -21 = -16.970562748 Simplifying x + -21 = -16.970562748 Reorder the terms: -21 + x = -16.970562748 Solving -21 + x = -16.970562748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -16.970562748 + 21 Combine like terms: -21 + 21 = 0 0 + x = -16.970562748 + 21 x = -16.970562748 + 21 Combine like terms: -16.970562748 + 21 = 4.029437252 x = 4.029437252 Simplifying x = 4.029437252Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.970562748, 4.029437252}
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