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Simplifying -16x2 + 22.3x + 2 = 0 Reorder the terms: 2 + 22.3x + -16x2 = 0 Solving 2 + 22.3x + -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'. -0.125 + -1.39375x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.39375x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.39375x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.39375x + x2 = 0 + 0.125 -1.39375x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.39375x + x2 = 0.125 The x term is -1.39375x. Take half its coefficient (-0.696875). Square it (0.4856347656) and add it to both sides. Add '0.4856347656' to each side of the equation. -1.39375x + 0.4856347656 + x2 = 0.125 + 0.4856347656 Reorder the terms: 0.4856347656 + -1.39375x + x2 = 0.125 + 0.4856347656 Combine like terms: 0.125 + 0.4856347656 = 0.6106347656 0.4856347656 + -1.39375x + x2 = 0.6106347656 Factor a perfect square on the left side: (x + -0.696875)(x + -0.696875) = 0.6106347656 Calculate the square root of the right side: 0.781431229 Break this problem into two subproblems by setting (x + -0.696875) equal to 0.781431229 and -0.781431229.Subproblem 1
x + -0.696875 = 0.781431229 Simplifying x + -0.696875 = 0.781431229 Reorder the terms: -0.696875 + x = 0.781431229 Solving -0.696875 + x = 0.781431229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.696875' to each side of the equation. -0.696875 + 0.696875 + x = 0.781431229 + 0.696875 Combine like terms: -0.696875 + 0.696875 = 0.000000 0.000000 + x = 0.781431229 + 0.696875 x = 0.781431229 + 0.696875 Combine like terms: 0.781431229 + 0.696875 = 1.478306229 x = 1.478306229 Simplifying x = 1.478306229Subproblem 2
x + -0.696875 = -0.781431229 Simplifying x + -0.696875 = -0.781431229 Reorder the terms: -0.696875 + x = -0.781431229 Solving -0.696875 + x = -0.781431229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.696875' to each side of the equation. -0.696875 + 0.696875 + x = -0.781431229 + 0.696875 Combine like terms: -0.696875 + 0.696875 = 0.000000 0.000000 + x = -0.781431229 + 0.696875 x = -0.781431229 + 0.696875 Combine like terms: -0.781431229 + 0.696875 = -0.084556229 x = -0.084556229 Simplifying x = -0.084556229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.478306229, -0.084556229}
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