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Simplifying x2 + 3x = 910 Reorder the terms: 3x + x2 = 910 Solving 3x + x2 = 910 Solving for variable 'x'. Reorder the terms: -910 + 3x + x2 = 910 + -910 Combine like terms: 910 + -910 = 0 -910 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '910' to each side of the equation. -910 + 3x + 910 + x2 = 0 + 910 Reorder the terms: -910 + 910 + 3x + x2 = 0 + 910 Combine like terms: -910 + 910 = 0 0 + 3x + x2 = 0 + 910 3x + x2 = 0 + 910 Combine like terms: 0 + 910 = 910 3x + x2 = 910 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 = 910 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 910 + 2.25 Combine like terms: 910 + 2.25 = 912.25 2.25 + 3x + x2 = 912.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 912.25 Calculate the square root of the right side: 30.203476621 Break this problem into two subproblems by setting (x + 1.5) equal to 30.203476621 and -30.203476621.Subproblem 1
x + 1.5 = 30.203476621 Simplifying x + 1.5 = 30.203476621 Reorder the terms: 1.5 + x = 30.203476621 Solving 1.5 + x = 30.203476621 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 = 30.203476621 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 30.203476621 + -1.5 x = 30.203476621 + -1.5 Combine like terms: 30.203476621 + -1.5 = 28.703476621 x = 28.703476621 Simplifying x = 28.703476621Subproblem 2
x + 1.5 = -30.203476621 Simplifying x + 1.5 = -30.203476621 Reorder the terms: 1.5 + x = -30.203476621 Solving 1.5 + x = -30.203476621 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 = -30.203476621 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -30.203476621 + -1.5 x = -30.203476621 + -1.5 Combine like terms: -30.203476621 + -1.5 = -31.703476621 x = -31.703476621 Simplifying x = -31.703476621Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.703476621, -31.703476621}
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