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Simplifying -16x2 + 4x + 13 = 0 Reorder the terms: 13 + 4x + -16x2 = 0 Solving 13 + 4x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.8125 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.8125' to each side of the equation. -0.8125 + -0.25x + 0.8125 + x2 = 0 + 0.8125 Reorder the terms: -0.8125 + 0.8125 + -0.25x + x2 = 0 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.8125 -0.25x + x2 = 0 + 0.8125 Combine like terms: 0 + 0.8125 = 0.8125 -0.25x + x2 = 0.8125 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.8125 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.8125 + 0.015625 Combine like terms: 0.8125 + 0.015625 = 0.828125 0.015625 + -0.25x + x2 = 0.828125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.828125 Calculate the square root of the right side: 0.910013736 Break this problem into two subproblems by setting (x + -0.125) equal to 0.910013736 and -0.910013736.Subproblem 1
x + -0.125 = 0.910013736 Simplifying x + -0.125 = 0.910013736 Reorder the terms: -0.125 + x = 0.910013736 Solving -0.125 + x = 0.910013736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.910013736 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.910013736 + 0.125 x = 0.910013736 + 0.125 Combine like terms: 0.910013736 + 0.125 = 1.035013736 x = 1.035013736 Simplifying x = 1.035013736Subproblem 2
x + -0.125 = -0.910013736 Simplifying x + -0.125 = -0.910013736 Reorder the terms: -0.125 + x = -0.910013736 Solving -0.125 + x = -0.910013736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.910013736 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.910013736 + 0.125 x = -0.910013736 + 0.125 Combine like terms: -0.910013736 + 0.125 = -0.785013736 x = -0.785013736 Simplifying x = -0.785013736Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.035013736, -0.785013736}
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