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Simplifying x2 + 3x + -870 = 0 Reorder the terms: -870 + 3x + x2 = 0 Solving -870 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '870' to each side of the equation. -870 + 3x + 870 + x2 = 0 + 870 Reorder the terms: -870 + 870 + 3x + x2 = 0 + 870 Combine like terms: -870 + 870 = 0 0 + 3x + x2 = 0 + 870 3x + x2 = 0 + 870 Combine like terms: 0 + 870 = 870 3x + x2 = 870 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 = 870 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 870 + 2.25 Combine like terms: 870 + 2.25 = 872.25 2.25 + 3x + x2 = 872.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 872.25 Calculate the square root of the right side: 29.533878851 Break this problem into two subproblems by setting (x + 1.5) equal to 29.533878851 and -29.533878851.Subproblem 1
x + 1.5 = 29.533878851 Simplifying x + 1.5 = 29.533878851 Reorder the terms: 1.5 + x = 29.533878851 Solving 1.5 + x = 29.533878851 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 = 29.533878851 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 29.533878851 + -1.5 x = 29.533878851 + -1.5 Combine like terms: 29.533878851 + -1.5 = 28.033878851 x = 28.033878851 Simplifying x = 28.033878851Subproblem 2
x + 1.5 = -29.533878851 Simplifying x + 1.5 = -29.533878851 Reorder the terms: 1.5 + x = -29.533878851 Solving 1.5 + x = -29.533878851 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 = -29.533878851 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -29.533878851 + -1.5 x = -29.533878851 + -1.5 Combine like terms: -29.533878851 + -1.5 = -31.033878851 x = -31.033878851 Simplifying x = -31.033878851Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.033878851, -31.033878851}
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