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Simplifying x2 + 3x + 10 = 90 Reorder the terms: 10 + 3x + x2 = 90 Solving 10 + 3x + x2 = 90 Solving for variable 'x'. Reorder the terms: 10 + -90 + 3x + x2 = 90 + -90 Combine like terms: 10 + -90 = -80 -80 + 3x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -80 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 3x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 3x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 3x + x2 = 0 + 80 3x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 3x + x2 = 80 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 80 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 80 + 2.25 Combine like terms: 80 + 2.25 = 82.25 2.25 + 3x + x2 = 82.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + 1.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + 1.5 = 9.069178574 Simplifying x + 1.5 = 9.069178574 Reorder the terms: 1.5 + x = 9.069178574 Solving 1.5 + x = 9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.069178574 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.069178574 + -1.5 x = 9.069178574 + -1.5 Combine like terms: 9.069178574 + -1.5 = 7.569178574 x = 7.569178574 Simplifying x = 7.569178574Subproblem 2
x + 1.5 = -9.069178574 Simplifying x + 1.5 = -9.069178574 Reorder the terms: 1.5 + x = -9.069178574 Solving 1.5 + x = -9.069178574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.069178574 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.069178574 + -1.5 x = -9.069178574 + -1.5 Combine like terms: -9.069178574 + -1.5 = -10.569178574 x = -10.569178574 Simplifying x = -10.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.569178574, -10.569178574}
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