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Simplifying -4x2 + -27x = -45 Reorder the terms: -27x + -4x2 = -45 Solving -27x + -4x2 = -45 Solving for variable 'x'. Reorder the terms: 45 + -27x + -4x2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + -27x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.25 + 6.75x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 6.75x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 6.75x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 6.75x + x2 = 0 + 11.25 6.75x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 6.75x + x2 = 11.25 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = 11.25 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 11.25 + 11.390625 Combine like terms: 11.25 + 11.390625 = 22.640625 11.390625 + 6.75x + x2 = 22.640625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 22.640625 Calculate the square root of the right side: 4.758216578 Break this problem into two subproblems by setting (x + 3.375) equal to 4.758216578 and -4.758216578.Subproblem 1
x + 3.375 = 4.758216578 Simplifying x + 3.375 = 4.758216578 Reorder the terms: 3.375 + x = 4.758216578 Solving 3.375 + x = 4.758216578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 4.758216578 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 4.758216578 + -3.375 x = 4.758216578 + -3.375 Combine like terms: 4.758216578 + -3.375 = 1.383216578 x = 1.383216578 Simplifying x = 1.383216578Subproblem 2
x + 3.375 = -4.758216578 Simplifying x + 3.375 = -4.758216578 Reorder the terms: 3.375 + x = -4.758216578 Solving 3.375 + x = -4.758216578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -4.758216578 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -4.758216578 + -3.375 x = -4.758216578 + -3.375 Combine like terms: -4.758216578 + -3.375 = -8.133216578 x = -8.133216578 Simplifying x = -8.133216578Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.383216578, -8.133216578}
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