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Simplifying 4x2 + -12x2 = 9x + -27 Combine like terms: 4x2 + -12x2 = -8x2 -8x2 = 9x + -27 Reorder the terms: -8x2 = -27 + 9x Solving -8x2 = -27 + 9x Solving for variable 'x'. Reorder the terms: 27 + -9x + -8x2 = -27 + 9x + 27 + -9x Reorder the terms: 27 + -9x + -8x2 = -27 + 27 + 9x + -9x Combine like terms: -27 + 27 = 0 27 + -9x + -8x2 = 0 + 9x + -9x 27 + -9x + -8x2 = 9x + -9x Combine like terms: 9x + -9x = 0 27 + -9x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.375 + 1.125x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 1.125x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 1.125x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 1.125x + x2 = 0 + 3.375 1.125x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 1.125x + x2 = 3.375 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 3.375 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 3.375 + 0.31640625 Combine like terms: 3.375 + 0.31640625 = 3.69140625 0.31640625 + 1.125x + x2 = 3.69140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 3.69140625 Calculate the square root of the right side: 1.921303269 Break this problem into two subproblems by setting (x + 0.5625) equal to 1.921303269 and -1.921303269.Subproblem 1
x + 0.5625 = 1.921303269 Simplifying x + 0.5625 = 1.921303269 Reorder the terms: 0.5625 + x = 1.921303269 Solving 0.5625 + x = 1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.921303269 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.921303269 + -0.5625 x = 1.921303269 + -0.5625 Combine like terms: 1.921303269 + -0.5625 = 1.358803269 x = 1.358803269 Simplifying x = 1.358803269Subproblem 2
x + 0.5625 = -1.921303269 Simplifying x + 0.5625 = -1.921303269 Reorder the terms: 0.5625 + x = -1.921303269 Solving 0.5625 + x = -1.921303269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.921303269 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.921303269 + -0.5625 x = -1.921303269 + -0.5625 Combine like terms: -1.921303269 + -0.5625 = -2.483803269 x = -2.483803269 Simplifying x = -2.483803269Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.358803269, -2.483803269}
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