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Simplifying x2 + 3x + -65 = 0 Reorder the terms: -65 + 3x + x2 = 0 Solving -65 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 3x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 3x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 3x + x2 = 0 + 65 3x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 3x + x2 = 65 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 = 65 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 65 + 2.25 Combine like terms: 65 + 2.25 = 67.25 2.25 + 3x + x2 = 67.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + 1.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + 1.5 = 8.200609733 Simplifying x + 1.5 = 8.200609733 Reorder the terms: 1.5 + x = 8.200609733 Solving 1.5 + x = 8.200609733 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 = 8.200609733 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.200609733 + -1.5 x = 8.200609733 + -1.5 Combine like terms: 8.200609733 + -1.5 = 6.700609733 x = 6.700609733 Simplifying x = 6.700609733Subproblem 2
x + 1.5 = -8.200609733 Simplifying x + 1.5 = -8.200609733 Reorder the terms: 1.5 + x = -8.200609733 Solving 1.5 + x = -8.200609733 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 = -8.200609733 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.200609733 + -1.5 x = -8.200609733 + -1.5 Combine like terms: -8.200609733 + -1.5 = -9.700609733 x = -9.700609733 Simplifying x = -9.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.700609733, -9.700609733}
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