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Simplifying x2 + 3x = 20x + 90 Reorder the terms: 3x + x2 = 20x + 90 Reorder the terms: 3x + x2 = 90 + 20x Solving 3x + x2 = 90 + 20x Solving for variable 'x'. Reorder the terms: -90 + 3x + -20x + x2 = 90 + 20x + -90 + -20x Combine like terms: 3x + -20x = -17x -90 + -17x + x2 = 90 + 20x + -90 + -20x Reorder the terms: -90 + -17x + x2 = 90 + -90 + 20x + -20x Combine like terms: 90 + -90 = 0 -90 + -17x + x2 = 0 + 20x + -20x -90 + -17x + x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -90 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -17x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -17x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -17x + x2 = 0 + 90 -17x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -17x + x2 = 90 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 90 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 90 + 72.25 Combine like terms: 90 + 72.25 = 162.25 72.25 + -17x + x2 = 162.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + -8.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + -8.5 = 12.737739203 Simplifying x + -8.5 = 12.737739203 Reorder the terms: -8.5 + x = 12.737739203 Solving -8.5 + x = 12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 12.737739203 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 12.737739203 + 8.5 x = 12.737739203 + 8.5 Combine like terms: 12.737739203 + 8.5 = 21.237739203 x = 21.237739203 Simplifying x = 21.237739203Subproblem 2
x + -8.5 = -12.737739203 Simplifying x + -8.5 = -12.737739203 Reorder the terms: -8.5 + x = -12.737739203 Solving -8.5 + x = -12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -12.737739203 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -12.737739203 + 8.5 x = -12.737739203 + 8.5 Combine like terms: -12.737739203 + 8.5 = -4.237739203 x = -4.237739203 Simplifying x = -4.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.237739203, -4.237739203}
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