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Simplifying 5x2 + 12x + -9 = x2 + -9x + 3 Reorder the terms: -9 + 12x + 5x2 = x2 + -9x + 3 Reorder the terms: -9 + 12x + 5x2 = 3 + -9x + x2 Solving -9 + 12x + 5x2 = 3 + -9x + x2 Solving for variable 'x'. Reorder the terms: -9 + -3 + 12x + 9x + 5x2 + -1x2 = 3 + -9x + x2 + -3 + 9x + -1x2 Combine like terms: -9 + -3 = -12 -12 + 12x + 9x + 5x2 + -1x2 = 3 + -9x + x2 + -3 + 9x + -1x2 Combine like terms: 12x + 9x = 21x -12 + 21x + 5x2 + -1x2 = 3 + -9x + x2 + -3 + 9x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -12 + 21x + 4x2 = 3 + -9x + x2 + -3 + 9x + -1x2 Reorder the terms: -12 + 21x + 4x2 = 3 + -3 + -9x + 9x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -12 + 21x + 4x2 = 0 + -9x + 9x + x2 + -1x2 -12 + 21x + 4x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 -12 + 21x + 4x2 = 0 + x2 + -1x2 -12 + 21x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + 21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 5.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 5.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5.25x + x2 = 0 + 3 5.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 5.25x + x2 = 3 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 3 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 3 + 6.890625 Combine like terms: 3 + 6.890625 = 9.890625 6.890625 + 5.25x + x2 = 9.890625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 9.890625 Calculate the square root of the right side: 3.144936406 Break this problem into two subproblems by setting (x + 2.625) equal to 3.144936406 and -3.144936406.Subproblem 1
x + 2.625 = 3.144936406 Simplifying x + 2.625 = 3.144936406 Reorder the terms: 2.625 + x = 3.144936406 Solving 2.625 + x = 3.144936406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 3.144936406 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 3.144936406 + -2.625 x = 3.144936406 + -2.625 Combine like terms: 3.144936406 + -2.625 = 0.519936406 x = 0.519936406 Simplifying x = 0.519936406Subproblem 2
x + 2.625 = -3.144936406 Simplifying x + 2.625 = -3.144936406 Reorder the terms: 2.625 + x = -3.144936406 Solving 2.625 + x = -3.144936406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -3.144936406 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -3.144936406 + -2.625 x = -3.144936406 + -2.625 Combine like terms: -3.144936406 + -2.625 = -5.769936406 x = -5.769936406 Simplifying x = -5.769936406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.519936406, -5.769936406}
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