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Simplifying 2x2 + 30x + -73 = 0 Reorder the terms: -73 + 30x + 2x2 = 0 Solving -73 + 30x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + 15x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + 15x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + 15x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + 15x + x2 = 0 + 36.5 15x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 15x + x2 = 36.5 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 36.5 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 36.5 + 56.25 Combine like terms: 36.5 + 56.25 = 92.75 56.25 + 15x + x2 = 92.75 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 92.75 Calculate the square root of the right side: 9.630680142 Break this problem into two subproblems by setting (x + 7.5) equal to 9.630680142 and -9.630680142.Subproblem 1
x + 7.5 = 9.630680142 Simplifying x + 7.5 = 9.630680142 Reorder the terms: 7.5 + x = 9.630680142 Solving 7.5 + x = 9.630680142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.630680142 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.630680142 + -7.5 x = 9.630680142 + -7.5 Combine like terms: 9.630680142 + -7.5 = 2.130680142 x = 2.130680142 Simplifying x = 2.130680142Subproblem 2
x + 7.5 = -9.630680142 Simplifying x + 7.5 = -9.630680142 Reorder the terms: 7.5 + x = -9.630680142 Solving 7.5 + x = -9.630680142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.630680142 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.630680142 + -7.5 x = -9.630680142 + -7.5 Combine like terms: -9.630680142 + -7.5 = -17.130680142 x = -17.130680142 Simplifying x = -17.130680142Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.130680142, -17.130680142}
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