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Simplifying x2 + 3x + -10 = 85 Reorder the terms: -10 + 3x + x2 = 85 Solving -10 + 3x + x2 = 85 Solving for variable 'x'. Reorder the terms: -10 + -85 + 3x + x2 = 85 + -85 Combine like terms: -10 + -85 = -95 -95 + 3x + x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -95 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 3x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 3x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 3x + x2 = 0 + 95 3x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 3x + x2 = 95 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 = 95 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 95 + 2.25 Combine like terms: 95 + 2.25 = 97.25 2.25 + 3x + x2 = 97.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + 1.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + 1.5 = 9.861541462 Simplifying x + 1.5 = 9.861541462 Reorder the terms: 1.5 + x = 9.861541462 Solving 1.5 + x = 9.861541462 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 = 9.861541462 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.861541462 + -1.5 x = 9.861541462 + -1.5 Combine like terms: 9.861541462 + -1.5 = 8.361541462 x = 8.361541462 Simplifying x = 8.361541462Subproblem 2
x + 1.5 = -9.861541462 Simplifying x + 1.5 = -9.861541462 Reorder the terms: 1.5 + x = -9.861541462 Solving 1.5 + x = -9.861541462 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 = -9.861541462 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.861541462 + -1.5 x = -9.861541462 + -1.5 Combine like terms: -9.861541462 + -1.5 = -11.361541462 x = -11.361541462 Simplifying x = -11.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.361541462, -11.361541462}
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