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Simplifying x2 + -42x + -0.5 = 0 Reorder the terms: -0.5 + -42x + x2 = 0 Solving -0.5 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -42x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -42x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -42x + x2 = 0 + 0.5 -42x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -42x + x2 = 0.5 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 = 0.5 + 441 Reorder the terms: 441 + -42x + x2 = 0.5 + 441 Combine like terms: 0.5 + 441 = 441.5 441 + -42x + x2 = 441.5 Factor a perfect square on the left side: (x + -21)(x + -21) = 441.5 Calculate the square root of the right side: 21.011901389 Break this problem into two subproblems by setting (x + -21) equal to 21.011901389 and -21.011901389.Subproblem 1
x + -21 = 21.011901389 Simplifying x + -21 = 21.011901389 Reorder the terms: -21 + x = 21.011901389 Solving -21 + x = 21.011901389 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 = 21.011901389 + 21 Combine like terms: -21 + 21 = 0 0 + x = 21.011901389 + 21 x = 21.011901389 + 21 Combine like terms: 21.011901389 + 21 = 42.011901389 x = 42.011901389 Simplifying x = 42.011901389Subproblem 2
x + -21 = -21.011901389 Simplifying x + -21 = -21.011901389 Reorder the terms: -21 + x = -21.011901389 Solving -21 + x = -21.011901389 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 = -21.011901389 + 21 Combine like terms: -21 + 21 = 0 0 + x = -21.011901389 + 21 x = -21.011901389 + 21 Combine like terms: -21.011901389 + 21 = -0.011901389 x = -0.011901389 Simplifying x = -0.011901389Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.011901389, -0.011901389}
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