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Simplifying 4x2 + 27x + -4 = 0 Reorder the terms: -4 + 27x + 4x2 = 0 Solving -4 + 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'. -1 + 6.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 6.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6.75x + x2 = 0 + 1 6.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 6.75x + x2 = 1 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 = 1 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 1 + 11.390625 Combine like terms: 1 + 11.390625 = 12.390625 11.390625 + 6.75x + x2 = 12.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 12.390625 Calculate the square root of the right side: 3.52003196 Break this problem into two subproblems by setting (x + 3.375) equal to 3.52003196 and -3.52003196.Subproblem 1
x + 3.375 = 3.52003196 Simplifying x + 3.375 = 3.52003196 Reorder the terms: 3.375 + x = 3.52003196 Solving 3.375 + x = 3.52003196 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 = 3.52003196 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 3.52003196 + -3.375 x = 3.52003196 + -3.375 Combine like terms: 3.52003196 + -3.375 = 0.14503196 x = 0.14503196 Simplifying x = 0.14503196Subproblem 2
x + 3.375 = -3.52003196 Simplifying x + 3.375 = -3.52003196 Reorder the terms: 3.375 + x = -3.52003196 Solving 3.375 + x = -3.52003196 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 = -3.52003196 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -3.52003196 + -3.375 x = -3.52003196 + -3.375 Combine like terms: -3.52003196 + -3.375 = -6.89503196 x = -6.89503196 Simplifying x = -6.89503196Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14503196, -6.89503196}
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