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Simplifying 4x2 + 27x + 28 = 0 Reorder the terms: 28 + 27x + 4x2 = 0 Solving 28 + 27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + 6.75x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6.75x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 6.75x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6.75x + x2 = 0 + -7 6.75x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 6.75x + x2 = -7 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 = -7 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = -7 + 11.390625 Combine like terms: -7 + 11.390625 = 4.390625 11.390625 + 6.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + 3.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + 3.375 = 2.095381827 Simplifying x + 3.375 = 2.095381827 Reorder the terms: 3.375 + x = 2.095381827 Solving 3.375 + x = 2.095381827 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 = 2.095381827 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 2.095381827 + -3.375 x = 2.095381827 + -3.375 Combine like terms: 2.095381827 + -3.375 = -1.279618173 x = -1.279618173 Simplifying x = -1.279618173Subproblem 2
x + 3.375 = -2.095381827 Simplifying x + 3.375 = -2.095381827 Reorder the terms: 3.375 + x = -2.095381827 Solving 3.375 + x = -2.095381827 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 = -2.095381827 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -2.095381827 + -3.375 x = -2.095381827 + -3.375 Combine like terms: -2.095381827 + -3.375 = -5.470381827 x = -5.470381827 Simplifying x = -5.470381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.279618173, -5.470381827}
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