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Simplifying x2 + -42x + -147 = 0 Reorder the terms: -147 + -42x + x2 = 0 Solving -147 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + -42x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + -42x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + -42x + x2 = 0 + 147 -42x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 -42x + x2 = 147 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 = 147 + 441 Reorder the terms: 441 + -42x + x2 = 147 + 441 Combine like terms: 147 + 441 = 588 441 + -42x + x2 = 588 Factor a perfect square on the left side: (x + -21)(x + -21) = 588 Calculate the square root of the right side: 24.248711306 Break this problem into two subproblems by setting (x + -21) equal to 24.248711306 and -24.248711306.Subproblem 1
x + -21 = 24.248711306 Simplifying x + -21 = 24.248711306 Reorder the terms: -21 + x = 24.248711306 Solving -21 + x = 24.248711306 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 = 24.248711306 + 21 Combine like terms: -21 + 21 = 0 0 + x = 24.248711306 + 21 x = 24.248711306 + 21 Combine like terms: 24.248711306 + 21 = 45.248711306 x = 45.248711306 Simplifying x = 45.248711306Subproblem 2
x + -21 = -24.248711306 Simplifying x + -21 = -24.248711306 Reorder the terms: -21 + x = -24.248711306 Solving -21 + x = -24.248711306 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 = -24.248711306 + 21 Combine like terms: -21 + 21 = 0 0 + x = -24.248711306 + 21 x = -24.248711306 + 21 Combine like terms: -24.248711306 + 21 = -3.248711306 x = -3.248711306 Simplifying x = -3.248711306Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.248711306, -3.248711306}
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