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Simplifying x * x + 3x = 510 Multiply x * x x2 + 3x = 510 Reorder the terms: 3x + x2 = 510 Solving 3x + x2 = 510 Solving for variable 'x'. Reorder the terms: -510 + 3x + x2 = 510 + -510 Combine like terms: 510 + -510 = 0 -510 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '510' to each side of the equation. -510 + 3x + 510 + x2 = 0 + 510 Reorder the terms: -510 + 510 + 3x + x2 = 0 + 510 Combine like terms: -510 + 510 = 0 0 + 3x + x2 = 0 + 510 3x + x2 = 0 + 510 Combine like terms: 0 + 510 = 510 3x + x2 = 510 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 = 510 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 510 + 2.25 Combine like terms: 510 + 2.25 = 512.25 2.25 + 3x + x2 = 512.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 512.25 Calculate the square root of the right side: 22.632940596 Break this problem into two subproblems by setting (x + 1.5) equal to 22.632940596 and -22.632940596.Subproblem 1
x + 1.5 = 22.632940596 Simplifying x + 1.5 = 22.632940596 Reorder the terms: 1.5 + x = 22.632940596 Solving 1.5 + x = 22.632940596 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 = 22.632940596 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 22.632940596 + -1.5 x = 22.632940596 + -1.5 Combine like terms: 22.632940596 + -1.5 = 21.132940596 x = 21.132940596 Simplifying x = 21.132940596Subproblem 2
x + 1.5 = -22.632940596 Simplifying x + 1.5 = -22.632940596 Reorder the terms: 1.5 + x = -22.632940596 Solving 1.5 + x = -22.632940596 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 = -22.632940596 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -22.632940596 + -1.5 x = -22.632940596 + -1.5 Combine like terms: -22.632940596 + -1.5 = -24.132940596 x = -24.132940596 Simplifying x = -24.132940596Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.132940596, -24.132940596}
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