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Simplifying 4x2 + 28x + -27 = 0 Reorder the terms: -27 + 28x + 4x2 = 0 Solving -27 + 28x + 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'. -6.75 + 7x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 7x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 7x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 7x + x2 = 0 + 6.75 7x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 7x + x2 = 6.75 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 6.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 6.75 + 12.25 Combine like terms: 6.75 + 12.25 = 19 12.25 + 7x + x2 = 19 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 3.5) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 3.5 = 4.358898944 Simplifying x + 3.5 = 4.358898944 Reorder the terms: 3.5 + x = 4.358898944 Solving 3.5 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.358898944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.358898944 + -3.5 x = 4.358898944 + -3.5 Combine like terms: 4.358898944 + -3.5 = 0.858898944 x = 0.858898944 Simplifying x = 0.858898944Subproblem 2
x + 3.5 = -4.358898944 Simplifying x + 3.5 = -4.358898944 Reorder the terms: 3.5 + x = -4.358898944 Solving 3.5 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.358898944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.358898944 + -3.5 x = -4.358898944 + -3.5 Combine like terms: -4.358898944 + -3.5 = -7.858898944 x = -7.858898944 Simplifying x = -7.858898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.858898944, -7.858898944}
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