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Simplifying x2 + 3x + -590 = 0 Reorder the terms: -590 + 3x + x2 = 0 Solving -590 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '590' to each side of the equation. -590 + 3x + 590 + x2 = 0 + 590 Reorder the terms: -590 + 590 + 3x + x2 = 0 + 590 Combine like terms: -590 + 590 = 0 0 + 3x + x2 = 0 + 590 3x + x2 = 0 + 590 Combine like terms: 0 + 590 = 590 3x + x2 = 590 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 = 590 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 590 + 2.25 Combine like terms: 590 + 2.25 = 592.25 2.25 + 3x + x2 = 592.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 592.25 Calculate the square root of the right side: 24.336187047 Break this problem into two subproblems by setting (x + 1.5) equal to 24.336187047 and -24.336187047.Subproblem 1
x + 1.5 = 24.336187047 Simplifying x + 1.5 = 24.336187047 Reorder the terms: 1.5 + x = 24.336187047 Solving 1.5 + x = 24.336187047 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 = 24.336187047 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 24.336187047 + -1.5 x = 24.336187047 + -1.5 Combine like terms: 24.336187047 + -1.5 = 22.836187047 x = 22.836187047 Simplifying x = 22.836187047Subproblem 2
x + 1.5 = -24.336187047 Simplifying x + 1.5 = -24.336187047 Reorder the terms: 1.5 + x = -24.336187047 Solving 1.5 + x = -24.336187047 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 = -24.336187047 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -24.336187047 + -1.5 x = -24.336187047 + -1.5 Combine like terms: -24.336187047 + -1.5 = -25.836187047 x = -25.836187047 Simplifying x = -25.836187047Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.836187047, -25.836187047}
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