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Simplifying 4x2 + -27x + -15 = 0 Reorder the terms: -15 + -27x + 4x2 = 0 Solving -15 + -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'. -3.75 + -6.75x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -6.75x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -6.75x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -6.75x + x2 = 0 + 3.75 -6.75x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -6.75x + x2 = 3.75 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 = 3.75 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 3.75 + 11.390625 Combine like terms: 3.75 + 11.390625 = 15.140625 11.390625 + -6.75x + x2 = 15.140625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (x + -3.375) equal to 3.891095604 and -3.891095604.Subproblem 1
x + -3.375 = 3.891095604 Simplifying x + -3.375 = 3.891095604 Reorder the terms: -3.375 + x = 3.891095604 Solving -3.375 + x = 3.891095604 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 = 3.891095604 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.891095604 + 3.375 x = 3.891095604 + 3.375 Combine like terms: 3.891095604 + 3.375 = 7.266095604 x = 7.266095604 Simplifying x = 7.266095604Subproblem 2
x + -3.375 = -3.891095604 Simplifying x + -3.375 = -3.891095604 Reorder the terms: -3.375 + x = -3.891095604 Solving -3.375 + x = -3.891095604 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 = -3.891095604 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.891095604 + 3.375 x = -3.891095604 + 3.375 Combine like terms: -3.891095604 + 3.375 = -0.516095604 x = -0.516095604 Simplifying x = -0.516095604Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.266095604, -0.516095604}
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