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Simplifying 612 = x2 + 3x Reorder the terms: 612 = 3x + x2 Solving 612 = 3x + x2 Solving for variable 'x'. Reorder the terms: 612 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 612 + -3x + -1x2 = 0 + x2 + -1x2 612 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 612 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -612 + 3x + x2 = 0 Move the constant term to the right: Add '612' to each side of the equation. -612 + 3x + 612 + x2 = 0 + 612 Reorder the terms: -612 + 612 + 3x + x2 = 0 + 612 Combine like terms: -612 + 612 = 0 0 + 3x + x2 = 0 + 612 3x + x2 = 0 + 612 Combine like terms: 0 + 612 = 612 3x + x2 = 612 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 = 612 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 612 + 2.25 Combine like terms: 612 + 2.25 = 614.25 2.25 + 3x + x2 = 614.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 614.25 Calculate the square root of the right side: 24.784067463 Break this problem into two subproblems by setting (x + 1.5) equal to 24.784067463 and -24.784067463.Subproblem 1
x + 1.5 = 24.784067463 Simplifying x + 1.5 = 24.784067463 Reorder the terms: 1.5 + x = 24.784067463 Solving 1.5 + x = 24.784067463 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 = 24.784067463 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 24.784067463 + -1.5 x = 24.784067463 + -1.5 Combine like terms: 24.784067463 + -1.5 = 23.284067463 x = 23.284067463 Simplifying x = 23.284067463Subproblem 2
x + 1.5 = -24.784067463 Simplifying x + 1.5 = -24.784067463 Reorder the terms: 1.5 + x = -24.784067463 Solving 1.5 + x = -24.784067463 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 = -24.784067463 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -24.784067463 + -1.5 x = -24.784067463 + -1.5 Combine like terms: -24.784067463 + -1.5 = -26.284067463 x = -26.284067463 Simplifying x = -26.284067463Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.284067463, -26.284067463}
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