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Simplifying -1x2 + 90x + 99 = 0 Reorder the terms: 99 + 90x + -1x2 = 0 Solving 99 + 90x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -99 + -90x + x2 = 0 Move the constant term to the right: Add '99' to each side of the equation. -99 + -90x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -90x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -90x + x2 = 0 + 99 -90x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -90x + x2 = 99 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = 99 + 2025 Reorder the terms: 2025 + -90x + x2 = 99 + 2025 Combine like terms: 99 + 2025 = 2124 2025 + -90x + x2 = 2124 Factor a perfect square on the left side: (x + -45)(x + -45) = 2124 Calculate the square root of the right side: 46.086874487 Break this problem into two subproblems by setting (x + -45) equal to 46.086874487 and -46.086874487.Subproblem 1
x + -45 = 46.086874487 Simplifying x + -45 = 46.086874487 Reorder the terms: -45 + x = 46.086874487 Solving -45 + x = 46.086874487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 46.086874487 + 45 Combine like terms: -45 + 45 = 0 0 + x = 46.086874487 + 45 x = 46.086874487 + 45 Combine like terms: 46.086874487 + 45 = 91.086874487 x = 91.086874487 Simplifying x = 91.086874487Subproblem 2
x + -45 = -46.086874487 Simplifying x + -45 = -46.086874487 Reorder the terms: -45 + x = -46.086874487 Solving -45 + x = -46.086874487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -46.086874487 + 45 Combine like terms: -45 + 45 = 0 0 + x = -46.086874487 + 45 x = -46.086874487 + 45 Combine like terms: -46.086874487 + 45 = -1.086874487 x = -1.086874487 Simplifying x = -1.086874487Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.086874487, -1.086874487}
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