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Simplifying 7 + -1x2 = -84x Solving 7 + -1x2 = -84x Solving for variable 'x'. Reorder the terms: 7 + 84x + -1x2 = -84x + 84x Combine like terms: -84x + 84x = 0 7 + 84x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -84x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -84x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -84x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -84x + x2 = 0 + 7 -84x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -84x + x2 = 7 The x term is -84x. Take half its coefficient (-42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. -84x + 1764 + x2 = 7 + 1764 Reorder the terms: 1764 + -84x + x2 = 7 + 1764 Combine like terms: 7 + 1764 = 1771 1764 + -84x + x2 = 1771 Factor a perfect square on the left side: (x + -42)(x + -42) = 1771 Calculate the square root of the right side: 42.083250825 Break this problem into two subproblems by setting (x + -42) equal to 42.083250825 and -42.083250825.Subproblem 1
x + -42 = 42.083250825 Simplifying x + -42 = 42.083250825 Reorder the terms: -42 + x = 42.083250825 Solving -42 + x = 42.083250825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = 42.083250825 + 42 Combine like terms: -42 + 42 = 0 0 + x = 42.083250825 + 42 x = 42.083250825 + 42 Combine like terms: 42.083250825 + 42 = 84.083250825 x = 84.083250825 Simplifying x = 84.083250825Subproblem 2
x + -42 = -42.083250825 Simplifying x + -42 = -42.083250825 Reorder the terms: -42 + x = -42.083250825 Solving -42 + x = -42.083250825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = -42.083250825 + 42 Combine like terms: -42 + 42 = 0 0 + x = -42.083250825 + 42 x = -42.083250825 + 42 Combine like terms: -42.083250825 + 42 = -0.083250825 x = -0.083250825 Simplifying x = -0.083250825Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.083250825, -0.083250825}
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