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Simplifying x2 + 3x + -570 = 0 Reorder the terms: -570 + 3x + x2 = 0 Solving -570 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '570' to each side of the equation. -570 + 3x + 570 + x2 = 0 + 570 Reorder the terms: -570 + 570 + 3x + x2 = 0 + 570 Combine like terms: -570 + 570 = 0 0 + 3x + x2 = 0 + 570 3x + x2 = 0 + 570 Combine like terms: 0 + 570 = 570 3x + x2 = 570 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 = 570 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 570 + 2.25 Combine like terms: 570 + 2.25 = 572.25 2.25 + 3x + x2 = 572.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 572.25 Calculate the square root of the right side: 23.921747428 Break this problem into two subproblems by setting (x + 1.5) equal to 23.921747428 and -23.921747428.Subproblem 1
x + 1.5 = 23.921747428 Simplifying x + 1.5 = 23.921747428 Reorder the terms: 1.5 + x = 23.921747428 Solving 1.5 + x = 23.921747428 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 = 23.921747428 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 23.921747428 + -1.5 x = 23.921747428 + -1.5 Combine like terms: 23.921747428 + -1.5 = 22.421747428 x = 22.421747428 Simplifying x = 22.421747428Subproblem 2
x + 1.5 = -23.921747428 Simplifying x + 1.5 = -23.921747428 Reorder the terms: 1.5 + x = -23.921747428 Solving 1.5 + x = -23.921747428 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 = -23.921747428 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -23.921747428 + -1.5 x = -23.921747428 + -1.5 Combine like terms: -23.921747428 + -1.5 = -25.421747428 x = -25.421747428 Simplifying x = -25.421747428Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.421747428, -25.421747428}
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